A367155 - OEIS

%I #12 Nov 10 2023 04:00:39

%S 1,1,5,56,948,21804,634284,22348584,925322784,44039346264,

%T 2369167375656,142173632632272,9416315321258928,682290228636729504,

%U 53689645309437175968,4559660591348115191808,415683140400707316145920,40490500091575002629253120

%N E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x).

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

%F a(n) ~ 9 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(n + 2/27)). - _Vaclav Kotesovec_, Nov 10 2023

%t Table[Sum[(3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 10 2023 *)

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

%Y Cf. A367158, A367161, A367164.

%Y Cf. A087152.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 07 2023