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%I #10 Sep 17 2022 08:50:09
%S 1,0,0,6,24,120,23760,327600,5201280,1283688000,37574409600,
%T 1219438281600,378254710310400,19092171351052800,1045282110435763200,
%U 394211859168070944000,30499777423295212032000,2523689643597315088896000,1125362204955051396299366400
%N a(n) = n! * Sum_{k=0..floor(n/3)} k^n/k!.
%F E.g.f.: Sum_{k>=0} (k * x)^(3 * k) / (k! * (1 - k * x)).
%o (PARI) a(n) = n!*sum(k=0, n\3, k^n/k!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^(3*k)/(k!*(1-k*x)))))
%Y Cf. A256016, A357191.
%Y Cf. A352982, A357194.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 17 2022
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