A349852 Expansion of Sum_{k>=0} k * x^k/(1 + k * x).

0, 1, 1, 0, 2, 1, -5, 20, -28, -47, 525, -2056, 3902, 9633, -129033, 664364, -1837904, -2388687, 67004697, -478198544, 1994889946, -1669470783, -56929813933, 615188040196, -3794477505572, 12028579019537, 50780206473221, -1172949397924184, 10766410530764118

Offset

0,5

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = -Sum_{k=0..n} (-k)^(n-k+1).

Mathematica

a[n_] := -Sum[(-k)^(n - k + 1), {k, 0, n}]; Array[a, 29, 0] (* Amiram Eldar, Dec 02 2021 *)

Prog

(PARI) a(n, s=1, 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*x^k/(1+k*x))))

Crossrefs

Cf. A038125, A349853, A349854, A349855, A349859, A349860, A349861.

Sequence in context: A012905 A254677 A184298 * A260701 A184300 A317390

Adjacent sequences: A349849 A349850 A349851 * A349853 A349854 A349855

Keyword

sign

Author

Seiichi Manyama, Dec 02 2021

Status

approved