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A191800 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(2*n^2). 4
1, 1, 3, 16, 109, 851, 7275, 66393, 637239, 6371848, 65961782, 703953599, 7722738071, 86924392498, 1002603956938, 11842465020207, 143208130730229, 1773099186411938, 22483740028949531, 292129222113885503, 3891268435685371911 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

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

(1) A = Sum_{n>=0} x^n*A^(2*n)*Product_{k=1..n} (1-x*A^(8*k-6))/(1-x*A^(8*k-2));

(2) A = 1/(1- A^2*x/(1- A^2*(A^4-1)*x/(1- A^10*x/(1- A^6*(A^8-1)*x/(1- A^18*x/(1- A^10*(A^12-1)*x/(1- A^26*x/(1- A^14*(A^16-1)*x/(1- ...))))))))) (continued fraction);

due to a q-series identity and an identity of a partial elliptic theta function, respectively.

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 109*x^4 + 851*x^5 + 7275*x^6 +...

where the g.f. satisfies:

A(x) = 1 + x*A(x)^2 + x^2*A(x)^8 + x^3*A(x)^18 + x^4*A(x)^32 +...+ x^n*A(x)^(2*n^2) +...

PROG

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

CROSSREFS

Cf. A107595, A191801, A191802, A191803, A191804.

Sequence in context: A135074 A292752 A220379 * A286764 A180609 A074540

Adjacent sequences:  A191797 A191798 A191799 * A191801 A191802 A191803

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 16 2011

STATUS

approved

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Last modified September 19 07:24 EDT 2020. Contains 337178 sequences. (Running on oeis4.)