A141761 Column 0 of triangle A141760.

1, 1, 1, 2, 6, 26, 154, 1188, 11474, 134432, 1863168, 29936846, 548625820, 11315025894, 259733293774, 6574304470320, 182050022755386, 5477819548007438, 178054691097463354, 6220193033111607018

Offset: 0

Author

Paul D. Hanna, Jul 18 2008

Keywords

• nonn

Comments

Also equals column 1 (shifted) of triangle A141760.

Crossrefs

Cf. A141760, A141762, A141763, A141764.

Programs

PARI

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

Formula

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

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