OFFSET
0,36
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
G.f.: Product_{k>=1} (1 - x^(5*k)) * (1 - x^(7*k)). - Seiichi Manyama, Oct 18 2016
Expansion of f(-x^5) * f(-x^7) in powers of x where f() is a Ramanujan theta function.
Euler transform of period 35 sequence [ 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, -2, ...]. - Michael Somos, Oct 19 2016
EXAMPLE
G.f. = 1 - x^5 - x^7 - x^10 + x^12 - x^14 + x^17 + x^19 + x^24 + x^25 - x^32 + ...
G.f. = q - q^11 - q^15 - q^21 + q^25 - q^29 + q^35 + q^39 + q^49 + q^51 - q^65 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^5] QPochhammer[ x^7], {x, 0, n}]; (* Michael Somos, Oct 21 2016 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^5 + A) * eta(x^7 + A), n))}; /* Michael Somos, Oct 19 2016 */
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved