

A246814


Expansion of phi(q) * phi(q^4)^2 in powers of q where phi() is a Ramanujan theta function.


2



1, 2, 0, 0, 2, 8, 0, 0, 4, 10, 0, 0, 8, 8, 0, 0, 6, 16, 0, 0, 8, 16, 0, 0, 8, 10, 0, 0, 0, 24, 0, 0, 12, 16, 0, 0, 10, 8, 0, 0, 8, 32, 0, 0, 24, 24, 0, 0, 8, 18, 0, 0, 8, 24, 0, 0, 16, 16, 0, 0, 0, 24, 0, 0, 6, 32, 0, 0, 16, 32, 0, 0, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions


FORMULA

Expansion of eta(q)^2 * eta(q^4)^4 / (eta(q^2) * eta(q^8)^2) in powers of q.
Euler transform of period 8 sequence [ 2, 1, 2, 5, 2, 1, 2, 3, ...].
a(n) = (1)^(mod(n,4) = 1) * A116597(n).
a(4*n + 2) = a(4*n + 3) = 0. a(4*n) = A212885(n). a(4*n + 1) = (1)^n * A005876(n).


EXAMPLE

G.f. = 1  2*q  2*q^4 + 8*q^5  4*q^8  10*q^9 + 8*q^12 + 8*q^13 + ...


MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q] EllipticTheta[ 4, 0, q^4]^2, {q, 0, n}]; Table[a[n], {n, 0, 80}]


PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^4 / (eta(x^2 + A) * eta(x^8 + A)^2), n))};


CROSSREFS

Cf. A005876, A116597, A212885.
Sequence in context: A066209 A284455 A300222 * A116597 A202496 A165664
Adjacent sequences: A246811 A246812 A246813 * A246815 A246816 A246817


KEYWORD

sign


AUTHOR

Michael Somos, Sep 03 2014


STATUS

approved



