A177341 - OEIS

%I #2 Mar 30 2012 18:37:21

%S 1,1,3,15,94,670,5199,42879,370532,3324129,30770131,292642516,

%T 2851110772,28396320852,288716877223,2994030992113,31652050802267,

%U 341066444176593,3746408312358063,41963633210168463,479546389644040335

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n(3n+1)/2).

%F Let A = g.f. A(x), then A satisfies:

%F A = Sum_{n>=0} x^n*A^(2n)*Product_{k=1..n} (1-x*A^(6k-4))/(1-x*A^(6k-1)) due to a q-series identity.

%F G.f. A(x) satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) = g.f. of A177340.

%e G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 94*x^4 + 670*x^5 + 5199*x^6 +...

%e A(x) = 1 + x*A(x)^2 + x^2*A(x)^7 + x^3*A(x)^15 + x^4*A(x)^26 +...

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(j*(3*j+1)/2)+x*O(x^n))); polcoeff(A, n)}

%Y Cf. A177340.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 06 2010