A389844 E.g.f. A(x) satisfies A(x) = exp(x^2 * A(x) / (1-x)^3).

1, 0, 2, 18, 180, 2280, 35400, 650160, 13797840, 332579520, 8981461440, 268753161600, 8829540941760, 316053530432640, 12245543006336640, 510672231381312000, 22809941762230022400, 1086565759159597516800, 54990339906059676518400, 2946763710646520705740800

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

E.g.f.: exp( -LambertW(-x^2 / (1-x)^3) ).

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

Mathematica

Table[n!*Sum[(k+1)^(k-1)*Binomial[n+k-1, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Oct 28 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n+k-1, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(k+1)^(k-1)* Binomial(n+k-1, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 28 2025

Crossrefs

Cf. A367789, A389847.

Cf. A376515, A389843.

Cf. A386514, A387949.

Sequence in context: A161122 A019581 A183285 * A359458 A129627 A279860

Adjacent sequences: A389841 A389842 A389843 * A389845 A389846 A389847

Keyword

nonn

Author

Seiichi Manyama, Oct 17 2025

Status

approved