A134091 Column 1 of triangle A134090.

1, 2, 9, 46, 285, 2021, 16023, 139812, 1326111, 13544857, 147880458, 1715413558, 21036674321, 271585117428, 3677831536291, 52081368845176, 769123715337395, 11816582501728389, 188470925178659344, 3114771205613655362

Offset: 0

Author

Paul D. Hanna, Oct 07 2007

Keywords

• nonn

Comments

Row n of triangle T=A134090 = row n of (I + D*C)^n for n>=0 where C denotes Pascal's triangle, I the identity matrix and D a matrix where D(n+1,n)=1 and zeros elsewhere.

Crossrefs

Cf. A134090; columns: A122455, A134092, A134093; A134094 (row sums); A048993 (S2).

Programs

PARI

a(n)=polcoeff(sum(k=0,n+1,binomial(n+1,k)*x^k/(1-k*x)/prod(i=0,k,1-i*x +x*O(x^n))),n)

Formula

a(n) = [x^n] Sum_{k=0..n+1} C(n+1,k)*x^k/(1-k*x) / [Product_{i=1..k}(1-i*x)].