A390062 E.g.f. A(x) satisfies A(x) = exp( x*A(x) / (1-x*A(x))^2 ) * (1-x*A(x)).

1, 0, 3, 16, 225, 3456, 70315, 1695744, 48085569, 1561600000, 57237686451, 2336950517760, 105202392163297, 5177074754912256, 276507345273046875, 15930573217475854336, 984840353514596357505, 65029954976871157334016, 4567942182903740505689059

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..350

Formula

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

E.g.f.: (1/x) * Series_Reversion( x * exp(-x / (1-x)^2) / (1-x) ).

Mathematica

Table[n!*Sum[(n+1)^(k-1)*Binomial[k-2, n-k]/k!, {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 05 2025 *)

Prog

(PARI) a(n, q=1, r=1, s=1, t=2, u=-1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);

Crossrefs

Cf. A364939, A380664.

Cf. A088695.

Sequence in context: A113597 A361366 A000273 * A071897 A182012 A272385

Adjacent sequences: A390059 A390060 A390061 * A390063 A390064 A390065

Keyword

nonn

Author

Seiichi Manyama, Oct 23 2025

Status

approved