A263538 Expansion of 3 * a(q^2) * b(q^2) * c(q^2) / (b(q) * c(q)^2) in powers of q where a(), b(), c() are cubic AGM theta functions.

1, 1, 6, 12, 5, 36, 60, 24, 150, 228, 86, 504, 732, 262, 1488, 2088, 725, 3996, 5460, 1852, 9972, 13344, 4436, 23472, 30876, 10103, 52644, 68268, 22040, 113364, 145224, 46336, 235734, 298800, 94378, 475488, 597108, 186926, 933672, 1162824, 361126, 1790028

Offset

0,3

Comments

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Formula

a(n) = A262930(2*n).

Example

G.f. = 1 + x + 6*x^2 + 12*x^3 + 5*x^4 + 36*x^5 + 60*x^6 + 24*x^7 + 150*x^8 +  ...

Mathematica

a:= With[{nmax = 50}, CoefficientList[Series[(QPochhammer[x^2]^3 + 9*x^2*QPochhammer[x^18]^3)*QPochhammer[x^2]^2*QPochhammer[x^6]/ (QPochhammer[x]*QPochhammer[x^3]^5), {x, 0, nmax}], x]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 31 2018 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^3 + 9 * x^2 * eta(x^18 + A)^3) * eta(x^2 + A)^2 * eta(x^6 + A) / (eta(x + A) * eta(x^3 + A)^5), n))};

Crossrefs

Cf. A262930.

Sequence in context: A066401 A335413 A356119 * A076590 A113660 A122859

Adjacent sequences: A263535 A263536 A263537 * A263539 A263540 A263541

Keyword

nonn

Author

Michael Somos, Oct 20 2015

Status

approved