A141764 Column 4 of triangle A141760.

1, 1, 5, 36, 336, 3863, 52944, 844777, 15411547, 316888806, 7258887646, 183464090374, 5074934980977, 152584140132667, 4956824851572271, 173086933804868142, 6467223731119047195, 257524741272166890188

Offset: 0

Author

Paul D. Hanna, Jul 18 2008

Keywords

• nonn

Crossrefs

Cf. A141760, A141761, A141762, A141763.

Programs

PARI

{a(n)=if(n==0,1,1 - sum(j=0,n-1,a(j)*(-1)^(n-j)*binomial((j+3)*(j+4)/2-6+n-j-1,n-j)))}

Formula

G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n/(1+x)^{(n+3)*(n+4)/2 - 6}.

a(n) = 1 - Sum_{j=0..n-1} a(j) * (-1)^(n-j) * C((j+3)(j+4)/2 + n-j-7, n-j) for n>0, with a(0)=1.