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%I #12 Sep 17 2022 08:48:43
%S 1,0,0,6,24,120,94372560,5284828080,338228714880,461220488356944960,
%T 124524904888012809600,36983489578531184304000,
%U 94262861823240343196388902400,78420937396722501660156363686400,70262981254649802508019882162611200
%N a(n) = n! * Sum_{k=0..floor(n/3)} k^(3*n)/k!.
%F E.g.f.: Sum_{k>=0} (k^3 * x)^(3 * k) / (k! * (1 - k^3 * x)).
%o (PARI) a(n) = n!*sum(k=0, n\3, k^(3*n)/k!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*x)^(3*k)/(k!*(1-k^3*x)))))
%Y Cf. A256016, A357193.
%Y Cf. A352984, A357192.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 17 2022
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