OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-1/3) * eta(q)^7 * eta(q^4)^7 * eta(q^6)^14 / (eta(q^2)^18 * eta(q^3)^5 * eta(q^12)^5) in powers of q.
Euler transform of period 12 sequence [ -7, 11, -2, 4, -7, 2, -7, 4, -2, 11, -7, 0, ...].
a(n) = A164269(3*n + 1).
EXAMPLE
G.f. = 1 - 7*x + 32*x^2 - 114*x^3 + 350*x^4 - 967*x^5 + 2468*x^6 + ...
G.f. = q - 7*q^4 + 32*q^7 - 114*q^10 + 350*q^13 - 967*q^16 + 2468*q^19 + ...
MATHEMATICA
f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A164270[n_] := SeriesCoefficient[(f[q^3, -q^6]^3*f[q^3, q^3])/( (f[q, -q^2])*f[q, q]^3), {q, 0, n}]; Table[A164270[n], {n, 0, 50}] (* G. C. Greubel, Sep 16 2017 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^7 * eta(x^4 + A)^7 * eta(x^6 + A)^14 / (eta(x^2 + A)^18 * eta(x^3 + A)^5 * eta(x^12 + A)^5), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 11 2009
STATUS
approved