A107888 Column 4 of triangle A107884.

1, 3, 18, 154, 1689, 22518, 353211, 6373053, 130079286, 2964644430, 74663152896, 2060033160771, 61821589542329, 2005535153907369, 69957741972993120, 2611812581931916545, 103938147849788867430, 4392991505873072541159

Offset: 0

Author

Paul D. Hanna, Jun 05 2005

Keywords

• nonn

Examples

			1 = 1*(1-x)^3 + 3*x*(1-x)^7 + 18*x^2*(1-x)^12 +
154*x^3*(1-x)^18 + 1689*x^4*(1-x)^25 + 22518*x^5*(1-x)^33 +...
		

Crossrefs

Cf. A107884, A107885, A107886, A107887.

Programs

Mathematica

a[ n_, k_: 0, j_: 3] := If[n < 1, Boole[n >= 0], a[ n, k, j] = Sum[ a[ n - 1, i, j + 1], {i, k + j}]]; (* Michael Somos, Nov 26 2016 *)

PARI

{a(n)=polcoeff(1-sum(k=0,n-1,a(k)*x^k*(1-x+x*O(x^n))^((k+3)*(k+4)/2-3)),n)}

Formula

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