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A349856
Expansion of Sum_{k>=0} x^k/(1 + k^2 * x).
5
1, 1, 0, -2, 7, 3, -242, 2032, -3795, -187211, 3860140, -36467310, -284357501, 21796446487, -538332144294, 5605176351652, 182065102478857, -12963817679287959, 422751776737348504, -5483284328996107802, -327213964461103956801, 30082452646697648945899
OFFSET
0,4
LINKS
FORMULA
a(n) = Sum_{k=0..n} (-k^2)^(n-k).
MATHEMATICA
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 *)
PROG
(PARI) a(n, s=0, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^2*x)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Dec 02 2021
STATUS
approved