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%I #10 Feb 22 2023 10:20:11
%S 1,1,1,2,5,11,29,81,229,696,2181,7045,23653,81433,288173,1046814,
%T 3887749,14768783,57275541,226462801,912443397,3741515804,15603500797,
%U 66134448329,284660214181,1243605590897,5511058189989,24760003963802,112726590916645
%N Expansion of Sum_{k>=0} ( x / (1 - k * x^2) )^k.
%F a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^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)^k*binomial(n-k-1, k));
%Y Cf. A324158, A360782.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Feb 21 2023
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