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Expansion of Sum_{k>=0} x^k/(1 + k^4 * x).
5

%I #18 Dec 11 2021 04:29:33

%S 1,1,0,-14,175,2211,-400994,25610260,582496701,-666933657755,

%T 166042332973276,-14222991979095594,-14297382182023795925,

%U 12622343477815735821511,-5840589387156997753180230,-443718496524920696265166664,5189349322544398120691167482361

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

%H Seiichi Manyama, <a href="/A349858/b349858.txt">Table of n, a(n) for n = 0..196</a>

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

%t a[n_] := Sum[If[k == n - k == 0, 1, (-k^4)^(n-k)], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Dec 03 2021 *)

%o (PARI) a(n, s=0, t=4) = sum(k=0, n, (-k^t)^(n-k)*k^s);

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^4*x)))

%Y Cf. A349856, A349857.

%K sign

%O 0,4

%A _Seiichi Manyama_, Dec 02 2021