A387995 E.g.f. A(x) satisfies A(x) = exp( x^3*A(x)^3 * (1+x*A(x))^3 ).

1, 0, 0, 6, 72, 360, 3240, 120960, 2721600, 42336000, 958003200, 35925120000, 1180279900800, 34173890150400, 1221040941120000, 54499683100262400, 2374836035539968000, 101298356772028416000, 4876716764520650649600, 263239997284712448000000

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..380

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A376477, A387994.

Cf. A389407.

Sequence in context: A361571 A389821 A389788 * A282817 A274955 A177468

Adjacent sequences: A387992 A387993 A387994 * A387996 A387997 A387998

Keyword

nonn

Author

Seiichi Manyama, Oct 13 2025

Status

approved