|
%I #7 Nov 02 2014 12:36:52
%S 1,1,3,12,65,419,3088,25557,233687,2331092,25130877,290632455,
%T 3583432896,46864388137,647273948043,9406216355420,143356121222905,
%U 2284850518224363,37988158312023376,657378186247162493,11816449728615690079,220230214060016856164
%N G.f.: Sum_{n>=0} x^n / Product_{k=0..n} (1 - (2*k-1)*x)^2.
%C Compare to o.g.f. of Dowling numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - (2*k-1)*x).
%H Vaclav Kotesovec, <a href="/A216373/b216373.txt">Table of n, a(n) for n = 0..300</a>
%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 65*x^4 + 419*x^5 + 3088*x^6 +...
%e where
%e 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 +...
%o (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)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A216367, A007405.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 05 2012
|
