A141762 Column 2 of triangle A141760.

1, 1, 3, 13, 77, 594, 5737, 67216, 931584, 14968423, 274312910, 5657512947, 129866646887, 3287152235160, 91025011377693, 2738909774003719, 89027345548731677, 3110096516555803509, 116244489639439112395

Offset: 0

Author

Paul D. Hanna, Jul 18 2008

Keywords

• nonn

Crossrefs

Cf. A141760, A141761, A141763, A141764.

Programs

PARI

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

Formula

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

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