A134092 Column 2 of triangle A134090.

1, 3, 18, 110, 780, 6167, 53494, 504030, 5112090, 55411697, 638154165, 7770348170, 99618149267, 1339889000543, 18848892749144, 276573551651632, 4222814264496510, 66947348027905977, 1099955438013660173

Offset

0,2

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.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = [x^n] Sum_{k=0..n+2} C(n+2,k)*x^k/(1-k*x)^2 / [Product_{i=1..k}(1-i*x)].

Prog

(PARI) {a(n)= polcoeff(sum(k=0, n+2, binomial(n+2, k)*x^k/(1-k*x)^2/prod(i=0, k, 1-i*x +x*O(x^n))), n)}

Crossrefs

Cf. A134090; columns: A122455, A134091, A134093; A134094 (row sums); A048993 (S2).

Sequence in context: A037655 A074571 A114311 * A000274 A207321 A193236

Adjacent sequences: A134089 A134090 A134091 * A134093 A134094 A134095

Keyword

nonn

Author

Paul D. Hanna, Oct 08 2007

Status

approved