A387993 E.g.f. A(x) satisfies A(x) = exp( x^2*A(x)^2 * (1+x*A(x))^3 ).

1, 0, 2, 18, 132, 2280, 43680, 887040, 23541840, 700358400, 22965798240, 856454860800, 35056060079040, 1561950195886080, 75824330662080000, 3966882851015884800, 222517085777437651200, 13341309681212242329600, 850759982500883840985600, 57498727204343513088000000

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..368

Formula

E.g.f.: (1/x) * Series_Reversion( x * exp(-x^2 * (1+x)^3) ).

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

Mathematica

Table[n!*Sum[(n+1)^(k-1)*Binomial[3*k, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 06 2025 *)

Prog

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

Crossrefs

Cf. A376476, A387992.

Cf. A365034, A387973.

Sequence in context: A363662 A064447 A043022 * A057971 A360132 A073512

Adjacent sequences: A387990 A387991 A387992 * A387994 A387995 A387996

Keyword

nonn

Author

Seiichi Manyama, Oct 13 2025

Status

approved