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A260547 Expansion of psi(x^3) * psi(-x^3) * chi(-x) / phi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions. 1
1, 3, 8, 19, 41, 83, 160, 296, 530, 923, 1569, 2611, 4264, 6848, 10833, 16904, 26049, 39683, 59817, 89286, 132064, 193683, 281800, 406955, 583577, 831323, 1176841, 1656096, 2317416, 3225472, 4466466, 6154859, 8442088, 11527811, 15674377, 21225403, 28629545 (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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-17/24) * eta(q^2) * eta(q^6) * eta(q^12) / eta(q)^3 in powers of q.

Euler transform of period 12 sequence [ 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 0, ...].

2 * a(n) = A001935(3*n + 2).

a(n) ~ exp(Pi*sqrt(3*n/2)) / (2^(15/4) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 15 2017

EXAMPLE

G.f. = 1 + 3*x + 8*x^2 + 19*x^3 + 41*x^4 + 83*x^5 + 160*x^6 + 296*x^7 + ...

G.f. = q^17 + 3*q^41 + 8*q^65 + 19*q^89 + 41*q^113 + 83*q^137 + 160*q^161 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2] QPochhammer[ x^6] QPochhammer[ x^12] / QPochhammer[ x]^3, {x, 0, n}];

PROG

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

CROSSREFS

Cf. A001935.

Sequence in context: A136396 A006380 A328540 * A328541 A182818 A095846

Adjacent sequences:  A260544 A260545 A260546 * A260548 A260549 A260550

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 28 2015

STATUS

approved

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Last modified August 19 06:22 EDT 2022. Contains 356216 sequences. (Running on oeis4.)