OFFSET
1,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..2500 (terms 1..77 from Michael Somos)
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
EXAMPLE
G.f. = q - 2*q^3 - 2*q^4 + 2*q^6 + 2*q^7 + 4*q^8 - q^9 - 2*q^10 - 2*q^13 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ q QPochhammer[ q^3, -q^4] QPochhammer[ -q, -q^4] QPochhammer[ -q^4] QPochhammer[ q] QPochhammer[ q^4] QPochhammer[ q^16], {q, 0, n}];
PROG
(PARI) {a(n) = my(A, m); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^16 + A) * sum( k=0, n, if( issquare( 8*k + 1, &m), (-1)^((m\2 + 2) \ 4) * x^k, 0), A), n))};
(Sage) CuspForms( Gamma1(16), 2, prec=78).0;
(Magma) Basis( CuspForms( Gamma1(16), 2), 78)[1];
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 02 2013
STATUS
approved