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

Author

Paul D. Hanna, Apr 05 2008

Keywords

• nonn

Crossrefs

Cf. A138909.

Programs

Mathematica

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

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]}

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