A192619 - OEIS

A192619

G.f. satisfies: A(x) = Product_{n>=1} (1 + x^n*A(x)^(1/2))^2/(1 - x^n*A(x)^(1/2))^2.

%I #8 Jul 19 2013 05:07:26

%S 1,4,20,104,556,3048,17064,97216,562036,3289836,19461448,116178600,

%T 699045176,4235292680,25816944176,158223753376,974389668364,

%U 6026623271840,37420762694588,233179517592232,1457706542138344,9139698522931008

%N G.f. satisfies: A(x) = Product_{n>=1} (1 + x^n*A(x)^(1/2))^2/(1 - x^n*A(x)^(1/2))^2.

%F Self-convolution of A190862.

%e G.f.: A(x) = 1 + 4*x + 20*x^2 + 104*x^3 + 556*x^4 + 3048*x^5 +...

%e The g.f. A = A(x) satisfies:

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

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=prod(m=1, n, (1+x^m*A^(1/2))^2/(1-x^m*A^(1/2)+x*O(x^n))^2));polcoeff(A, n)}

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=(1+sum(m=1, n, x^m*A^(m/2)*prod(k=1, m,(1+x^(k-1))/(1-x^k+x*O(x^n)))))^2); polcoeff(A, n)}

%Y Cf. A190862.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 06 2011