OFFSET
0,3
COMMENTS
LINKS
Seiichi Manyama, 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^(-5/8) * eta(q^8)^2 / eta(q) in powers of q.
Euler transform of period 8 sequence [ 1, 1, 1, 1, 1, 1, 1, -1, ...].
2 * a(n) = A132965(2*n + 1).
EXAMPLE
G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 20*x^8 + ...
G.f. = q^5 + q^13 + 2*q^21 + 3*q^29 + 5*q^37 + 7*q^45 + 11*q^53 + 15*q^61 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^8]^2 / QPochhammer[ x], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^8 + A)^2 / eta(x + A), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 09 2015
STATUS
approved