A209935 - OEIS

%I #6 Mar 30 2012 18:37:38

%S 1,1,5,66,1735,77587,5339632,527780778,71236904519,12635518401687,

%T 2857729962091681,804340796768258860,276170316701087964628,

%U 113757566198465278521124,55424247710747076665462268,31554099393732823158673973698

%N G.f.: 1 = Sum_{n>=0} a(n)*x^n*Product_{k=1..n+1} (1-k^2*x) for n>0 with a(0)=1.

%e G.f.: 1 = 1*(1-x) + 1*x*(1-x)*(1-2^2*x) + 5*x^2*(1-x)*(1-2^2*x)*(1-3^2*x) + 66*x^3*(1-x)*(1-2^2*x)*(1-3^2*x)*(1-4^2*x) + 1735*x^4*(1-x)*(1-2^2*x)*(1-3^2*x)*(1-4^2*x)*(1-5^2*x) +...

%o (PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k*prod(j=1, k+1, 1-j^2*x+x*O(x^n))), n))}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A082161.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 15 2012