A138912 Inverse binomial transform of A138911.

1, 1, 2, 9, 28, 145, 726, 4249, 27000, 186561, 1387450, 11034001, 93295236, 834720913, 7870851366, 77943848025, 808159323376, 8749874083585, 98687599614450, 1157060036429857, 14075106913366140, 177337182574590801, 2310567819180310558, 31087556340427928617

Offset: 0

Author

Paul D. Hanna, Apr 05 2008

Keywords

• nonn

Comments

The n-th term of the n-th inverse binomial transform of A138911 is 1 for n>=0.

Crossrefs

Cf. A138911 (binomial transform).

Programs

PARI

{a(n)=local(A=[1]);for(k=1,n,A=concat(A,0); A[k+1]=1-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) = 1 for n>=0.

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