A377340 - OEIS

%I #19 Oct 27 2024 01:39:39

%S 1,3,9,54,531,6498,101925,1920222,42251391,1067567850,30411486441,

%T 965077330374,33764590958571,1291198144146498,53587639922183757,

%U 2398901329112787630,115225387686206361495,5911249981088653607898,322592377196349009882513

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

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377348.

%F a(n) = 3 * Sum_{k=0..floor((3*n+3)/4)} (3*n-3*k+2)!/(3*n-4*k+3)! * Stirling2(n,k).

%o (PARI) a(n) = 3*sum(k=0, (3*n+3)\4, (3*n-3*k+2)!/(3*n-4*k+3)!*stirling(n, k, 2));

%Y Cf. A377326, A377339.

%Y Cf. A377348.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 26 2024