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%I #17 Feb 21 2023 02:09:24
%S 1,1,1,3,7,16,45,125,363,1127,3561,11696,39727,138113,494213,1811075,
%T 6784115,25985928,101520833,404305549,1640002039,6767576175,
%U 28395916893,121048681024,523902418555,2300906314849,10248029334297,46266088140291
%N Expansion of Sum_{k>=0} x^k / (1 - k*x^2)^(k+1).
%F a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-k,k).
%t Join[{1}, Table[Sum[Binomial[n-k,k] * (n-2*k)^k, {k,0,n/2}], {n,1,30}]] (* _Vaclav Kotesovec_, Feb 21 2023 *)
%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)^(k+1)))
%o (PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*binomial(n-k, k));
%Y Cf. A000248, A360783.
%Y Cf. A000045, A360592.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Feb 20 2023
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