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A260546 Expansion of phi(-x^3) * psi(-x^3) / phi(-x)^2 in powers of x where phi(), psi() are Ramanujan theta functions 1
1, 4, 12, 29, 64, 132, 258, 484, 876, 1539, 2636, 4416, 7256, 11716, 18624, 29190, 45164, 69060, 104457, 156416, 232044, 341256, 497804, 720648, 1035792, 1478720, 2097612, 2957590, 4146284, 5781120, 8018821, 11067748, 15203904, 20791590, 28310028, 38387556 (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^(-3/8) * eta(q^2)^2 * eta(q^3)^3 * eta(q^12) / (eta(q)^4 * eta(q^6)^2) in powers of q.

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

a(n) = A001935(3*n + 1).

a(n) ~ exp(Pi*sqrt(3*n/2)) / (2^(11/4) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 15 2017

EXAMPLE

G.f. = 1 + 4*x + 12*x^2 + 29*x^3 + 64*x^4 + 132*x^5 + 258*x^6 + 484*x^7 + ...

G.f. = q^3 + 4*q^11 + 12*q^19 + 29*q^27 + 64*q^35 + 132*q^43 + 258*q^51 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 / (EllipticTheta[ 4, 0, x]^2 EllipticTheta[ 4, 0, x^6]), {x, 0, n}];

PROG

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

CROSSREFS

Cf. A001935.

Sequence in context: A128563 A227085 A192978 * A062421 A036889 A036895

Adjacent sequences:  A260543 A260544 A260545 * A260547 A260548 A260549

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 28 2015

STATUS

approved

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Last modified October 22 22:22 EDT 2020. Contains 337962 sequences. (Running on oeis4.)