[seqfan] Sums of at most k distinct positive n-th powers.

[peter.luschny]

Howdy SeqFans!

SDPP[k](n) :<=> Sums of at most k distinct positive n-th powers.
(Is there a nice (n,k)-triangle in OEIS?)

SDPP[2](2) <-- ?
SDPP[2](3) <-- A114090
SDPP[2](4) <-- A004831
SDPP[2](5) <-- A004842

My question is: Is the proposition below true or not?

/
| If a(n) has the Eulerian generating function [1]
|     G_n(t) = A_n(t) (1 + t^4) / (1 - t)^(n + 1)
| then a(n) is a subsequence of SDPP(n).
\

For example n=4, G_4(t) = -(t^4+1)*(t+1)*(t^2+10*t+1)/(t-1)^5,
a(i) = 1,16,81,256,626,1312,2482,4352,7186,11296,17042,..

Cheers, Peter

[1] http://oeis.org/wiki/Eulerian_polynomials#Eulerian_generating_functions