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A355468 Expansion of Sum_{k>=0} (k^2 * x/(1 - k^2 * x))^k.

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%I A355468 #15 Feb 22 2023 08:03:34
%S A355468 1,1,17,858,85988,14318320,3570592512,1245401343760,578840603221568,
%T A355468 345763649636940672,258099498410703320960,235426611021544158413824,
%U A355468 257654470061373320338925568,333210260028337620911268462592
%N A355468 Expansion of Sum_{k>=0} (k^2 * x/(1 - k^2 * x))^k.
%H A355468 Winston de Greef, <a href="/A355468/b355468.txt">Table of n, a(n) for n = 0..211</a>
%F A355468 a(n) = Sum_{k=1..n} k^(2*n) * binomial(n-1,k-1) for n > 0.
%o A355468 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x/(1-k^2*x))^k))
%o A355468 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(2*n)*binomial(n-1, k-1)));
%Y A355468 Cf. A195242, A242446, A249459.
%K A355468 nonn
%O A355468 0,3
%A A355468 _Seiichi Manyama_, Jul 03 2022