A107879 Column 3 of triangle A107876.

1, 1, 4, 26, 230, 2565, 34516, 544423, 9857583, 201664780, 4603336725, 116059191472, 3204682702923, 96226940232235, 3122975927539860, 108970956192622980, 4069312064491308140, 161969813446983961395, 6846708764857861662741, 306381118887919045527510

Offset: 0

Author

Paul D. Hanna, Jun 04 2005

Keywords

• nonn

Examples

			1 = 1*(1-x)^1 + 1*x*(1-x)^4 + 4*x^2*(1-x)^8 + 26*x^3*(1-x)^13 + 230*x^4*(1-x)^19 + 2565*x^5*(1-x)^26 + 34516*x^6*(1-x)^34 +...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..389

Crossrefs

Cf. A107876, A107877, A107878.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(j-1)*
      (-1)^(n-j)*binomial((j+1)*(j+2)/2-2, n-j+1), j=1..n))
    end:
seq(a(n), n=0..22);  # Alois P. Heinz, Jul 10 2022

PARI

{a(n)=polcoeff(1-sum(k=0,n-1,a(k)*x^k*(1-x+x*O(x^n))^((k+2)*(k+3)/2-2)),n)}

Formula

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