OFFSET
0,3
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^(1/24) * eta(q^4)^5 / (eta(q) * eta(q^2)^2 * eta(q^8)^2) in powers of q.
Euler transform of period 8 sequence [ 1, 3, 1, -2, 1, 3, 1, 0, ...].
G.f.: (Sum_{k in Z} x^(2*k^2)) / (Product_{k>0} (1 - x^k)).
G.f. A(x) satisfies A(x^2) = ( chi(x)^2 + chi(-x)^2 )/2, where chi(x) = Product_{k >= 0} 1 + x^(2*k+1) is the g.f. of A000700. Cf. A226635. - Peter Bala, Sep 29 2023
EXAMPLE
1 + x + 4*x^2 + 5*x^3 + 9*x^4 + 13*x^5 + 21*x^6 + 29*x^7 + 46*x^8 + 62*x^9 + ...
1/q + q^23 + 4*q^47 + 5*q^71 + 9*q^95 + 13*q^119 + 21*q^143 + 29*q^167 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^2] / QPochhammer[ q], {q, 0, n}]
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^5 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^2), n))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Aug 31 2013
STATUS
approved