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%I #9 Feb 22 2023 10:20:26
%S 1,1,1,2,9,29,113,613,3033,17010,110929,713249,5061097,38762873,
%T 302389553,2544613578,22404995001,203762678941,1960880744337,
%U 19509713674397,201306862742217,2166901479447194,24018963506471921,275731857268608673,3271769647891351705
%N Expansion of Sum_{k>=0} ( x / (1 - (k * x)^2) )^k.
%F a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k) * binomial(n-k-1,k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-(k*x)^2))^k))
%o (PARI) a(n) = sum(k=0, n\2, (n-2*k)^(2*k)*binomial(n-k-1, k));
%Y Cf. A339481, A360787.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Feb 21 2023