A389817 E.g.f. A(x) satisfies A(x) = (1+x) * exp(x^2 * A(x)).

1, 1, 2, 12, 60, 540, 5160, 61320, 855120, 13320720, 237867840, 4665608640, 101253620160, 2394972740160, 61392422931840, 1697241718972800, 50273022678278400, 1590115688152992000, 53462198961358387200, 1904512774179375360000, 71658001164295350604800

Offset

0,3

Links

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

Formula

E.g.f.: -LambertW(-x^2 * (1+x))/x^2.

E.g.f.: (1+x) * exp( -LambertW(-x^2 * (1+x)) ).

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

Mathematica

Table[n!*Sum[(k+1)^(k-1)*Binomial[k+1, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 01 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(k+1, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(k+1)^(k-1)* Binomial(k+1, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Nov 01 2025

Crossrefs

Cf. A377826, A389820.

Cf. A376517.

Sequence in context: A362244 A393921 A362238 * A372986 A190425 A386983

Adjacent sequences: A389814 A389815 A389816 * A389818 A389819 A389820

Keyword

nonn

Author

Seiichi Manyama, Oct 16 2025

Status

approved