A191814 - OEIS

%I #4 Mar 30 2012 18:37:26

%S 1,1,1,1,2,18,154,970,4862,20879,83672,353281,1773612,11060634,

%T 84779040,772415014,7726721969,77774342729,747754441850,6734769291340,

%U 56695273838174,448350981091266,3357088027977272,24017325363442968

%N  G.f. satisfies: A(x) = Sum_{n>=0} x^(n^2)*A(x)^(n^4).

%e  G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 18*x^5 + 154*x^6 + 970*x^7 +...

%e where the g.f. satisfies:

%e A(x) = 1 + x*A(x) + x^4*A(x)^16 + x^9*A(x)^81 + x^16*A(x)^256 + x^25*A(x)^625 + x^36*A(x)^1296 +...+ x^(n^2)*A(x)^(n^4) +...

%o  (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^(m^2)*(A+x*O(x^n))^(m^4)));polcoeff(A,n)}

%Y  Cf. A157134, A157136, A191813.

%K nonn

%O 0,5

%A _Paul D. Hanna_, Jun 17 2011