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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
LINKS
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
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 20 2015
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)