OFFSET
0,4
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^(1/2) * eta(q^2) * eta(q^8) * eta(q^12)^2 / (eta(q) * eta(q^4) * eta(q^6) * eta(q^24)) in powers of q.
Euler transform of period 24 sequence [ 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, ...].
a(n) = A003105(2*n + 1).
EXAMPLE
G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 6*x^6 + 8*x^7 + 10*x^8 + 14*x^9 + ...
G.f. = 1/q + q + q^3 + 2*q^5 + 3*q^7 + 4*q^9 + 6*q^11 + 8*q^13 + 10*q^15 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2, x^12] QPochhammer[ x^10, x^12] QPochhammer[ x^12, x^24] QPochhammer[ x^8] / QPochhammer[x], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^8 + A) * eta(x^12 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^24 + A)), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 10 2015
STATUS
approved