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A260150 Expansion of f(x, x^5)^3 / (f(-x, -x^5) * f(-x^2, -x^2)^2) in powers of x where f(, ) is Ramanujan's general theta function. 1
1, 4, 11, 24, 48, 92, 170, 304, 526, 884, 1451, 2336, 3700, 5772, 8876, 13472, 20207, 29988, 44072, 64184, 92680, 132760, 188758, 266512, 373838, 521152, 722266, 995432, 1364684, 1861548, 2527224, 3415344, 4595497, 6157700, 8218050, 10925848, 14472520 (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

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of f(x) * psi(-x^3)^3 / (f(-x)^3 * psi(x^3)) in powers of x where psi(), f() are Ramanujan theta functions.

Euler transform of period 12 sequence [ 4, 1, 0, 2, 4, 2, 4, 2, 0, 1, 4, 0, ...].

a(n) = (-1)^n * A260057(n). a(n) = A261154(3*n + 2). a(2*n + 1) = 4 * A259033(n).

a(n) ~ exp(2*Pi*sqrt(n/3)) / (4*3^(5/4)*n^(3/4)). - Vaclav Kotesovec, Nov 16 2017

EXAMPLE

G.f. = 1 + 4*x + 11*x^2 + 24*x^3 + 48*x^4 + 92*x^5 + 170*x^6 + 304*x^7 + ...

G.f. = q^2 + 4*q^5 + 11*q^8 + 24*q^11 + 48*q^14 + 92*q^17 + 170*q^20 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 2^(-1/2) x^(-3/4) QPochhammer[ -x] / QPochhammer[x]^3 EllipticTheta[ 2, Pi/4, x^(3/2)]^3 / EllipticTheta[ 2, 0, x^(3/2)], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^3 + A)^4 * eta(x^12 + A)^3 / (eta(x + A)^4 * eta(x^4 + A) * eta(x^6 + A)^5), n))};

CROSSREFS

Cf. A259033, A260057, A261154.

Sequence in context: A143075 A290707 A260057 * A258472 A007678 A159350

Adjacent sequences:  A260147 A260148 A260149 * A260151 A260152 A260153

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 08 2015

STATUS

approved

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Last modified October 18 07:58 EDT 2018. Contains 316307 sequences. (Running on oeis4.)