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
Expansion of q^(1/4) * (eta(q^2)^9 / (eta(q)^5 * eta(q^4)^4))^2 in powers of q.
Euler transform of period 4 sequence [ 10, -8, 10, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (16 t)) = (1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A143894.
G.f.: (Product_{k>0} (1 + x^k)^5 / (1 + x^(2*k))^4)^2.
a(n) ~ exp(sqrt(2*n)*Pi) / (2^(9/4) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2015
EXAMPLE
G.f. = 1 + 10*x + 47*x^2 + 150*x^3 + 403*x^4 + 1002*x^5 + 2316*x^6 + 5004*x^7 + ...
G.f. = 1/q + 10*q^3 + 47*q^7 + 150*q^11 + 403*q^15 + 1002*q^19 + 2316*q^23 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2]^9 / (QPochhammer[ x]^5 QPochhammer[ x^4]^4))^2, {x, 0, n}]; (* Michael Somos, Apr 26 2015 *)
nmax = 40; CoefficientList[Series[Product[((1 + x^k)^5 / (1 + x^(2*k))^4)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^9 / (eta(x + A)^5 * eta(x^4 + A)^4))^2, n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 04 2008
STATUS
approved