OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 20 sequence [ 2, 1, 2, 1, 0, 0, 2, 3, 2, -2, 2, 3, 2, 0, 0, 1, 2, 1, 2, 0, ...].
a(n) = A132225(5*n + 1).
a(n) ~ exp(2*Pi*sqrt(n/5)) / (5^(5/4) * n^(3/4)). - Vaclav Kotesovec, Jul 04 2018
EXAMPLE
G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 14*x^4 + 22*x^5 + 35*x^6 + 54*x^7 + ...
G.f. = q + 2*q^6 + 4*q^11 + 8*q^16 + 14*q^21 + 22*q^26 + 35*q^31 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x^2, x^10] QPochhammer[ -x^8, x^10] (QPochhammer[ x^2, x^4] QPochhammer[ x^5] / QPochhammer[ x])^2, {x, 0, n}];
QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; A:= f[-x^5, -x^5]*f[x^2, x^8]/f[-x, - x^3]^2; a:= CoefficientList[Series[A, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 04 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[ 0, -2, -1, -2, -1, 0, 0, -2, -3, -2, 2, -2, -3, -2, 0, 0, -1, -2, -1, -2][k%20 + 1]), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 25 2015
STATUS
approved