A126443 a(n) = Sum_{k=0..n-1} C(n-1,k)*a(k)*2^k for n>0, with a(0)=1.

1, 1, 3, 17, 179, 3489, 127459, 8873137, 1195313043, 315321098561, 164239990789571, 169810102632595281, 349630019758589841523, 1436268949679165936016097, 11784559509424676876673518499, 193243076262167105764611875139569

Offset: 0

Author

Paul D. Hanna, Jan 01 2007

Keywords

• nonn

Comments

Generated by a generalization of a recurrence for the Bell numbers (A000110).

Starting with offset 1 = eigensequence of triangle A013609. - Gary W. Adamson, Sep 04 2009

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A126347, A000110.

Cf. A013609. - Gary W. Adamson, Sep 04 2009

Column k=2 of A306245.

Programs

PARI

a(n)=if(n==0,1,sum(k=0,n-1,binomial(n-1,k)*a(k)*2^k))

Formula

a(n) = Sum_{k=0..n*(n-1)/2} A126347(n,k)*2^k.

G.f. A(x) satisfies: A(x) = 1 + x*A(2*x/(1 - x))/(1 - x). - Ilya Gutkovskiy, Sep 02 2019

a(n) ~ c * 2^(n*(n-1)/2), where c = A081845 = 4.7684620580627434482997985... - Vaclav Kotesovec, Sep 16 2019