A349885 - OEIS

%I #12 Dec 04 2021 08:55:33

%S 1,1,3,-4,-218,4377,189549,-13317056,-283835940,117015022505,

%T -5604964950389,-1791024716075124,422751913131376674,

%U 8850160172208790801,-30082452518043880807911,7173002090013176579439392,1556433498641034120823054072

%N Expansion of Sum_{k>=0} (k * x)^k/(1 + k^3 * x).

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n-2*k).

%t a[n_] := Sum[If[k == 3*n - 2*k == 0, 1, (-1)^(n - k) * k^(3*n - 2*k)], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Dec 04 2021 *)

%o (PARI) a(n, t=3) = sum(k=0, n, (-k^t)^(n-k)*k^k);

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1+k^3*x)))

%Y Cf. A120485, A349884.

%K sign

%O 0,3

%A _Seiichi Manyama_, Dec 03 2021