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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
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
Sequence in context: A135074 A292752 A220379 * A286764 A180609 A074540
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 16 2011
STATUS
approved

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Last modified April 22 08:40 EDT 2024. Contains 371893 sequences. (Running on oeis4.)