A349856 - OEIS

%I #20 Dec 11 2021 04:29:36

%S 1,1,0,-2,7,3,-242,2032,-3795,-187211,3860140,-36467310,-284357501,

%T 21796446487,-538332144294,5605176351652,182065102478857,

%U -12963817679287959,422751776737348504,-5483284328996107802,-327213964461103956801,30082452646697648945899

%N Expansion of Sum_{k>=0} x^k/(1 + k^2 * x).

%H Seiichi Manyama, <a href="/A349856/b349856.txt">Table of n, a(n) for n = 0..343</a>

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

%t a[n_] := Sum[If[k == n - k == 0, 1, (-k^2)^(n - k)], {k, 0, n}]; Array[a, 22, 0] (* _Amiram Eldar_, Dec 03 2021 *)

%o (PARI) a(n, s=0, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^2*x)))

%Y Cf. A349857, A349858, A349889.

%K sign

%O 0,4

%A _Seiichi Manyama_, Dec 02 2021