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%I #9 Sep 24 2023 09:16:20
%S 1,1,2,6,24,144,1008,8064,72576,766080,8934912,113895936,1573254144,
%T 23864924160,389247344640,6786673496064,125855767166976,
%U 2492616008171520,52243870155079680,1154797100239749120,26835102086208159744,656159502089355264000
%N Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+1) / (4*k+1) ).
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} (4*k)! * binomial(n,4*k+1) * a(n-4*k-1).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+1)/(4*k+1)))))
%Y Cf. A296676, A365975, A365977.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 23 2023