A237653 O.g.f.: Sum_{n>=0} x^n*Product_{k=1..n} (k + x).

1, 1, 3, 9, 36, 176, 1030, 7039, 55098, 486346, 4780445, 51787405, 613045468, 7873065045, 109021348618, 1619197654575, 25675094145535, 432908683794379, 7733991639921585, 145933532935469016, 2900112108790279902, 60543749629794205640, 1324677739541613767983, 30312375400027348522996

Offset: 0

Author

Paul D. Hanna, May 11 2014

Keywords

• nonn

Comments

Equals antidiagonal sums of the triangle of unsigned Stirling numbers of the first kind (A008275).

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 36*x^4 + 176*x^5 + 1030*x^6 + 7039*x^7 +...
where
A(x) = 1 + x*(1+x) + x^2*(1+x)*(2+x) + x^3*(1+x)*(2+x)*(3+x) + x^4*(1+x)*(2+x)*(3+x)*(4+x) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A124380, A008275, A130534.

Programs

PARI

{a(n)=polcoeff(sum(k=0, n, x^k*prod(j=1, k, j+x +x*O(x^n))), n)}
for(n=0,30,print1(a(n),", "))