A349855 Expansion of Sum_{k>=0} k^4 * x^k/(1 + k * x).

0, 1, 15, 50, 76, 203, 335, -84, 2696, -3011, -8433, 130606, -662348, 1840439, 2391823, -67000872, 478203152, -1994884455, 1669477263, 56929821514, -615188031396, 3794477515715, -12028579007921, -50780206459996, 1172949397939160, -10766410530747243

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = Sum_{k=0..n} (-k)^(n-k+4).

Mathematica

a[n_] := Sum[(-k)^(n - k + 4), {k, 0, n}]; Array[a, 26, 0] (* Amiram Eldar, Dec 02 2021 *)

Prog

(PARI) a(n, s=4, t=1) = sum(k=0, n, (-k^t)^(n-k)*k^s);
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k^4*x^k/(1+k*x))))

Crossrefs

Cf. A038125, A349852, A349853, A349854.

Sequence in context: A199899 A020257 A298511 * A103777 A134742 A318084

Adjacent sequences: A349852 A349853 A349854 * A349856 A349857 A349858

Keyword

sign

Author

Seiichi Manyama, Dec 02 2021

Status

approved