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A224831 Expansion of phi(-x^3)^2 * psi(x) / chi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions. 1
1, 3, 5, 6, 5, 6, 7, 9, 11, 8, 9, 7, 11, 13, 8, 14, 11, 16, 14, 9, 14, 7, 18, 19, 12, 13, 10, 21, 19, 17, 21, 10, 15, 17, 17, 15, 14, 26, 20, 13, 18, 22, 21, 26, 17, 20, 13, 20, 30, 9, 24, 21, 26, 21, 13, 25, 20, 27, 30, 21, 17, 20, 35, 28, 18, 22, 16, 29, 25 (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 q^(-5/24) * eta(q^2)^4 * eta(q^3)^4 / (eta(q)^3 * eta(q^6)^2) in powers of q.

Euler transform of period 6 sequence [ 3, -1, -1, -1, 3, -3, ...].

a(n) = A224823(3*n).

EXAMPLE

1 + 3*x + 5*x^2 + 6*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 9*x^7 + 11*x^8 + 8*x^9 + ...

q^5 + 3*q^29 + 5*q^53 + 6*q^77 + 5*q^101 + 6*q^125 + 7*q^149 + 9*q^173 + ...

MATHEMATICA

a[n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^3]^2 EllipticTheta[ 2, 0, q^(1/2)]/(2 q^(1/8) QPochhammer[q, q^2]^2), {q, 0, n}]

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^3 + A)^4 / (eta(x + A)^3 * eta(x^6 + A)^2), n))}

CROSSREFS

Cf. A224823.

Sequence in context: A081498 A110279 A161435 * A281591 A267884 A077859

Adjacent sequences:  A224828 A224829 A224830 * A224832 A224833 A224834

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 21 2013

STATUS

approved

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)