A363356 - OEIS

%I #13 Aug 17 2023 08:16:05

%S 1,1,5,52,821,17536,473497,15476224,594230345,26221431808,

%T 1307680266221,72739285725184,4465197522732157,299855584017743872,

%U 21867349264346912705,1721013285639521959936,145394112130209844644113,13123788855563296766427136

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

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

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

%Y Cf. A088695, A362771, A363355.

%Y Cf. A365013.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 17 2023