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
Euler transform of period 10 sequence [ -2, 1, 0, -2, 0, -2, 0, 1, -2, 0, ...].
a(5*n + 4) = 0.
EXAMPLE
1 - 2*x + 2*x^2 - 2*x^3 + 2*x^5 - 4*x^6 + 6*x^7 - 4*x^8 + 6*x^10 - 12*x^11 + ...
MATHEMATICA
f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A215594[n_] := SeriesCoefficient[f[-x, -x^4]/f[x, x^4], {x, 0, n}]; Table[A215594[n], {n, 0, 50}] (* G. C. Greubel, Jun 18 2017 *)
PROG
(PARI) {a(n) = local(A, s); if( n<0, 0, A = x * O(x^n); s = sqrtint( 40*n + 9); polcoeff( sum( k=(-s + 6)\10, (s - 3)\10, (-1)^k * x^((5*k + 3)*k/2), A) / sum( k=(-s + 6)\10, (s - 3)\10, x^((5*k + 3)*k/2), A), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 16 2012
STATUS
approved