A216969 - OEIS

%I #7 Sep 21 2012 01:51:50

%S 1,1,1,2,5,17,51,199,653,2746,9506,41887,150209,683534,2513812,

%T 11714529,43913589,208460660,793362271,3822998161,14731492719,

%U 71883765642,279923388563,1380780426067,5426284435421,27023956574169,107069182011993,537876237669664

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

%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 17*x^5 + 51*x^6 + 199*x^7 +...

%e A(x)*A(-x) = 1 + x^2 + 7*x^4 + 74*x^6 + 967*x^8 + 14251*x^10 + 227037*x^12 +...

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

%o for(n=0,21,print1(a(n),", "))

%K nonn

%O 0,4

%A _Paul D. Hanna_, Sep 21 2012