A193319 - OEIS

%I #9 Oct 04 2020 11:30:23

%S 1,1,3,11,49,273,1859,14731,131073,1287041,13822051,161149227,

%T 2024636273,27227371345,389753084259,5912210812139,94679315407489,

%U 1595416629866625,28204870292970563,521740077282205387,10074781737635639601

%N G.f.: Sum_{n>=0} x^n*Product_{k=1..n} (1 - (4*k-3)*x) / (1 - (4*k-1)*x).

%H Vaclav Kotesovec, <a href="/A193319/b193319.txt">Table of n, a(n) for n = 0..250</a>

%e G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 49*x^4 + 273*x^5 + 1859*x^6 +...

%e where

%e A(x) =  1 + x*(1-x)/(1-3*x) + x^2*(1-x)*(1-5*x)/((1-3*x)*(1-7*x)) + x^3*(1-x)*(1-5*x)*(1-9*x)/((1-3*x)*(1-7*x)*(1-11*x)) +...

%o (PARI) {a(n)=polcoeff(sum(m=0,n,x^m*prod(k=1,m,(1-(4*k-3)*x)/(1-(4*k-1)*x +x*O(x^n)))),n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 22 2011