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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
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
Sequence in context: A338684 A304870 A361714 * A243672 A367424 A268653
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 16 2011
STATUS
approved

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Last modified May 24 23:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)