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Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(1/3).
2

%I #13 Aug 25 2024 09:57:51

%S 1,0,2,3,56,270,4824,44520,866816,12195792,267873120,5073187680,

%T 126754229568,2999710359360,85061489235072,2400155295632640,

%U 76724104598031360,2502434971473937920,89428428468644493312,3300036525511418327040

%N Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(1/3).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+1)) * |Stirling1(n-k,k)|/(n-k)!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(1/3)))

%o (PARI) a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+1)*abs(stirling(n-k, k, 1))/(n-k)!);

%Y Cf. A367879, A375689.

%Y Cf. A347015.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 24 2024