....I'm too lazy to break out the math again. But this is far closer to old Sejuani's damage output then new Sejuani, and remember, back when Sejuani was reworked, all the Sej fans were bitching about the reduction her in damage. Because it was visibly lower on her W and focused on her new E. Moreover they relied on a perfect AA reset use of Sejuani's W to keep her DPS up--and this is before the post rework patches gutted her damage repeatedly.
E's damage isn't exactly nerfed as its CD is almost halved at max rank. Optimal DPS, with an AP build will be considerably higher, but even without, she'll be able to reliably apply damage more often and keep targets in a state of almost-permaslow.
The big thing to note here is her W's initial hit+AA reset being where her damage is rooted is natural for her jungling. She'll do more damage then she did before with a single ability. I.E. Her damage at rank one with W, at level one, assuming she took Health Quints and Health Yellows and had at least 9 defense. (Which while not necessarily optimal, is something plenty of people do on Sej due to her passive armor buff. Moreover, starting with this extra bonus health favors her old W over her new one as its adding in a sizable chunk of bonus health.)
would be 4+12% HP on initial hit (its hard to figure math properly here, but as an example, lets say she's using it on a level 1 Anivia, the lowest health champion in the game at 468 HP, worst case scenario for Damage against a champion. Her new damage from W would be 4+56.16 magic damage+a total of 40+32.4 damage. Or, 132 magic damage. This is versus her old W damage in the same low-level health stacking scenario being 141.
Meaning, in the worst-case champ vs. Champ scenario, it is a nerf. In an average case, the %HP boost it into a buff, and in the jungle its a colossal buff to her first few camps.
As an example. Let's say Level 1 Sejuani starts Gromp for the poison armor. (she may also start Krugs, which is even more favorable as they have negative MR and high health both) her W will now chunk for 4+192 on the initial hit, +40+32 from her spin. Making her level 1 damage 268 from her W, vs. 132. Note: This is not single target damage. All additional damage, including the initial hit from her flail is AOE. The only portion of her W that is not AoE is the actual physical damage from her auto attack.
This means that her damage is straight up higher at level 1 in the jungle. It will also grow vastly in power as if she focuses W... As 12% total health scaling is huge.
Note her E is a shift, though. But maybe its just me, but I value near permaslow over rare heavy slows. Moreover, its damage is honestly higher now as it ranks up. Its damage is lower, but its CD decreases with each moment damage is distanced from her old E. Its higher DPS (slightly) and lower burst.
Moreover, I enjoy that Q isn't where your damage is located, this encourages Sejuani to use it as an escape--moreover, its value as CC is still present. Q was flat out nerfed. But she's up considerably in damage because of it. (The overall damage on Q is lower without the HP damage unless she's targeting like, Raptors or something, but her W has a much shorter CD (rank 1 CD is the same as rank 4 Q) and she can always, ALWAYS land her W AA after a Q (W can be activated mid jump and you can immediately auto on landing, so you can still get the burst-over-a-wall, actually its total damage is just higher now)
TL;DR: Sejuani's DPS is considerably higher, her Q is not where much of her damage is, favoring its use as an escape. Her W outperforms her old in everything but extreme early game against extremely low health targets. Her W outperforms her old Q in its same role as its CD is considerably shorter. (more damage) and her E doesn't actually have a damage nerf as its CD decreases as its base damage doesn't grow as fast, leading to similar DPS, lower burst (higher overal damage with AP as well) She is gettin a near permaslow at higher levels, and the ability to constantly keep Liandri's burning.
AKA: Buffs.