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^(-3/8) * eta(q^2)^2 * eta(q^3)^3 * eta(q^12) / (eta(q)^4 * eta(q^6)^2) in powers of q.
Euler transform of period 12 sequence [ 4, 2, 1, 2, 4, 1, 4, 2, 1, 2, 4, 0, ...].
a(n) = A001935(3*n + 1).
a(n) ~ exp(Pi*sqrt(3*n/2)) / (2^(11/4) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 15 2017
EXAMPLE
G.f. = 1 + 4*x + 12*x^2 + 29*x^3 + 64*x^4 + 132*x^5 + 258*x^6 + 484*x^7 + ...
G.f. = q^3 + 4*q^11 + 12*q^19 + 29*q^27 + 64*q^35 + 132*q^43 + 258*q^51 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 / (EllipticTheta[ 4, 0, x]^2 EllipticTheta[ 4, 0, x^6]), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A) / (eta(x + A)^4 * eta(x^6 + A)^2), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 28 2015
STATUS
approved