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A191804 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(6*n^2). 4
1, 1, 7, 82, 1221, 20718, 382315, 7489683, 153551487, 3264643144, 71545452946, 1609541143713, 37065029428453, 872037022019930, 20935244357544798, 512498682139660135, 12790021472251565047, 325439165493879484025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

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

(1) A = Sum_{n>=0} x^n*A^(6*n)*Product_{k=1..n} (1-x*A^(24*k-18))/(1-x*A^(24*k-6));

(2) A = 1/(1- A^6*x/(1- A^6*(A^12-1)*x/(1- A^30*x/(1- A^18*(A^24-1)*x/(1- A^54*x/(1- A^30*(A^36-1)*x/(1- A^78*x/(1- A^42*(A^48-1)*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 + 7*x^2 + 82*x^3 + 1221*x^4 + 20718*x^5 + 382315*x^6 +...

where the g.f. satisfies:

A(x) = 1 + x*A(x)^6 + x^2*A(x)^24 + x^3*A(x)^54 + x^4*A(x)^96 +...+ x^n*A(x)^(6*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))^(6*m^2))); polcoeff(A, n)}

CROSSREFS

Cf. A107595, A191800, A191801, A191802, A191803.

Sequence in context: A285062 A253265 A304870 * A243672 A268653 A242375

Adjacent sequences:  A191801 A191802 A191803 * A191805 A191806 A191807

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 16 2011

STATUS

approved

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Last modified August 4 19:32 EDT 2020. Contains 336202 sequences. (Running on oeis4.)