A386983 E.g.f. A(x) satisfies A(x) = exp(x^2 * (1+x)^2 * A(x)).

1, 0, 2, 12, 60, 720, 8400, 110880, 1883280, 34473600, 713543040, 16592083200, 419889476160, 11630725666560, 349278751261440, 11281197799872000, 390833564279558400, 14446005085396684800, 567444266540895744000, 23613207356724662476800, 1037560054360758197068800

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)^2) ).

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

Mathematica

Table[n!*Sum[(k+1)^(k-1)*Binomial[2*k, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 05 2025 *)

Prog

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

Crossrefs

Cf. A362772, A389787.

Cf. A387992.

Sequence in context: A389817 A372986 A190425 * A145630 A082688 A099996

Adjacent sequences: A386980 A386981 A386982 * A386984 A386985 A386986

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2025

Status

approved