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

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..21.

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.

Prog

(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]}

Crossrefs

Cf. A138911 (binomial transform).

Sequence in context: A291632 A328281 A324372 * A002747 A110377 A338436

Adjacent sequences: A138909 A138910 A138911 * A138913 A138914 A138915

Keyword

nonn

Author

Paul D. Hanna, Apr 05 2008

Status

approved