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A182031 Expansion of q^(-5/24) * (eta(q^3) * eta(q^6))^3 / (eta(q) * eta(q^2))^4 in powers of q. 1
1, 4, 18, 53, 163, 414, 1059, 2431, 5553, 11844, 25013, 50391, 100362, 193136, 367371, 680705, 1247247, 2238408, 3975218, 6941384, 12003156, 20465599, 34581525, 57737205, 95601892, 156665029, 254777220, 410580026, 657015874 (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).

REFERENCES

H.-C. Chan, On the Andrews-Schur proof of the Rogers-Ramanujan identities, Ramanujan J. 23 (2010), no. 1-3, 417-431. see p. 430 Theorem 7.

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 (psi(x^3) * phi(-x^3))^3 / (psi(x) * phi(-x))^4 in powers of x where phi(), psi() are Ramanujan theta functions.

Euler transform of period 6 sequence [ 4, 8, 1, 8, 4, 2, ...].

A002513(3*n + 2) = 3 * a(n).

EXAMPLE

1 + 4*x + 18*x^2 + 53*x^3 + 163*x^4 + 414*x^5 + 1059*x^6 + 2431*x^7 + ...

q^5 + 4*q^13 + 18*q^21 + 53*q^29 + 163*q^37 + 414*q^45 + 1059*q^53 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-5/8)*(eta[q^3]*eta[q^6])^3/(eta[q]*eta[q^2])^4, {q, 0, 100}], q] (* G. C. Greubel, Apr 16 2018 *)

PROG

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

(PARI) q='q+O('q^99); Vec((eta(q^3)*eta(q^6))^3/(eta(q)*eta(q^2))^4) \\ Altug Alkan, Apr 16 2018

CROSSREFS

Cf. A002513.

Sequence in context: A297945 A320544 A020644 * A212250 A229788 A242206

Adjacent sequences:  A182028 A182029 A182030 * A182032 A182033 A182034

KEYWORD

nonn

AUTHOR

Michael Somos, Apr 07 2012

STATUS

approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)