A134093 Column 3 of triangle A134090.

1, 4, 30, 215, 1729, 15176, 143814, 1462995, 15876410, 182811992, 2223580281, 28458251185, 381943459065, 5359649816728, 78430018675440, 1194057733357517, 18873870914263424, 309154787519651284, 5238840625331179517

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+3} C(n+3,k)*x^k/(1-k*x)^3 / [Product_{i=1..k}(1-i*x)].

Prog

(PARI) {a(n)= polcoeff(sum(k=0, n+3, binomial(n+3, k)*x^k/(1-k*x)^3/prod(i=0, k, 1-i*x +x*O(x^n))), n)}

Crossrefs

Cf. A134090; columns: A122455, A134091, A134092; A134094 (row sums); A048993 (S2).

Sequence in context: A272493 A246151 A094567 * A007905 A084976 A000313

Adjacent sequences: A134090 A134091 A134092 * A134094 A134095 A134096

Keyword

nonn

Author

Paul D. Hanna, Oct 08 2007

Status

approved