A216373 G.f.: Sum_{n>=0} x^n / Product_{k=0..n} (1 - (2*k-1)*x)^2.

1, 1, 3, 12, 65, 419, 3088, 25557, 233687, 2331092, 25130877, 290632455, 3583432896, 46864388137, 647273948043, 9406216355420, 143356121222905, 2284850518224363, 37988158312023376, 657378186247162493, 11816449728615690079, 220230214060016856164

Offset: 0

Author

Paul D. Hanna, Sep 05 2012

Keywords

• nonn

Comments

Compare to o.g.f. of Dowling numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - (2*k-1)*x).

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 65*x^4 + 419*x^5 + 3088*x^6 +...
where
A(x) = 1 + x/(1-x)^2 + x^2/((1-x)*(1-3*x))^2 + x^3/((1-x)*(1-3*x)*(1-5*x))^2 + x^4/((1-x)*(1-3*x)*(1-5*x)*(1-7*x))^2 +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A216367, A007405.

Programs

PARI

{a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-(2*k-1)*x +x*O(x^n))^2), n)}
for(n=0,30,print1(a(n),", "))