A389788 E.g.f. A(x) satisfies A(x) = exp(x^3 * (1+x)^3 * A(x)).

1, 0, 0, 6, 72, 360, 1800, 45360, 907200, 11854080, 168739200, 4191264000, 110509660800, 2481467788800, 59259443443200, 1805418821606400, 59339647471104000, 1879096682631168000, 62439211810412236800, 2346190339477714329600, 93866255690746226688000

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Formula

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

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

Mathematica

Table[n!*Sum[(k+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, (k+1)^(k-1)*binomial(3*k, n-3*k)/k!);

Crossrefs

Cf. A376145, A389786.

Cf. A387995.

Sequence in context: A276244 A361571 A389821 * A387995 A282817 A274955

Adjacent sequences: A389785 A389786 A389787 * A389789 A389790 A389791

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2025

Status

approved