A138910 Inverse binomial transform of A138909.

1, 1, 3, 20, 129, 1164, 12265, 151458, 2136337, 33901640, 597761361, 11593851510, 245310524041, 5622982528188, 138803996674057, 3671135646515834, 103568483199034785, 3104443346427521808, 98528857134710517793

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

O.g.f. satisfies: [x^n] A( x/(1+(n-1)*x) )/(1+(n-1)*x) = n! for n>=0.

E.g.f. satisfies: [x^n] A(x)*exp(-(n-1)*x) = 1 for n>=0.

E.g.f.: (x+1)/(exp(x)-x*exp(2*x)). - Vladimir Kruchinin, Nov 07 2016

a(n) ~ n! / LambertW(1)^(n-1). - Vaclav Kotesovec, Oct 30 2017

Mathematica

Range[0, 19]! CoefficientList[Series[(x + 1) / (Exp[x] - x Exp[2 x]), {x, 0, 19}], x] (* Vincenzo Librandi, Nov 07 2016 *)

Prog

(PARI) {a(n)=local(A=[1]); for(k=1, n, A=concat(A, 0); A[k+1]=k!-polcoeff(subst(Ser(A), x, x/(1+(k-1)*x+x*O(x^k)))/(1+(k-1)*x), k)); A[n+1]}

Crossrefs

Cf. A138909.

Sequence in context: A187442 A167590 A228884 * A000276 A216778 A337105

Adjacent sequences: A138907 A138908 A138909 * A138911 A138912 A138913

Keyword

nonn

Author

Paul D. Hanna, Apr 05 2008

Status

approved