A218295 G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(3*n^2).

1, 2, 14, 158, 2274, 37410, 670670, 12786622, 255519106, 5302716866, 113586849614, 2501007496542, 56446396937186, 1303401799574242, 30756416720161422, 741216834445478270, 18240706372460480002, 458484823574294544770, 11776969626284389958030

Offset

0,2

Comments

Given g.f. A(x), then Q = A(-x^2) satisfies:

Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^(3*k))/(1 + x*Q^(3*k))

due to a q-series expansion for the Jacobi theta_4 function.

Links

Table of n, a(n) for n=0..18.

Example

 G.f.: A(x) = 1 + 2*x + 14*x^2 + 158*x^3 + 2274*x^4 + 37410*x^5 +...
where
A(x) = 1 + 2*x*A(x)^3 + 2*x^2*A(x)^12 + 2*x^3*A(x)^27 + 2*x^4*A(x)^48 + ...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, 2*x^m*(A+x*O(x^n))^(3*m^2))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A176719, A218294.

Sequence in context: A332693 A196791 A349312 * A354242 A268011 A052112

Adjacent sequences: A218292 A218293 A218294 * A218296 A218297 A218298

Keyword

nonn

Author

Paul D. Hanna, Oct 26 2012

Status

approved