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A187428 Expansion of q^(-5/24) * eta(q^3)^3 / eta(q)^4 in powers of q. 3
1, 4, 14, 37, 93, 210, 454, 925, 1824, 3463, 6408, 11538, 20353, 35161, 59726, 99775, 164337, 266978, 428521, 679861, 1067415, 1659205, 2555617, 3902055, 5909867, 8881849, 13252334, 19637281, 28909989, 42297267, 61520450, 88976461, 127996994 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

FORMULA

Euler transform of period 3 sequence [ 4, 4, 1, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (576 t)) = 648^(-1/2) (t/i)^(-1/2) g(t) where q = exp(2 Pi i t) and g() is g.f. for A187427.

G.f.: Product_{k>0} (1 - x^(3*k))^3 / (1 - x^k)^4.

a(n) ~ exp(sqrt(2*n)*Pi)/(12*sqrt(3)*n). - Vaclav Kotesovec, Sep 07 2015

EXAMPLE

1 + 4*x + 14*x^2 + 37*x^3 + 93*x^4 + 210*x^5 + 454*x^6 + 925*x^7 + ...

q^5 + 4*q^29 + 14*q^53 + 37*q^77 + 93*q^101 + 210*q^125 + 454*q^149 + ...

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[(1 - x^(3*k))^3 / (1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2015 *)

eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-5/24) *eta[q^3]^3/eta[q]^4, {q, 0, 50}], q] (* G. C. Greubel, Aug 14 2018 *)

PROG

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

CROSSREFS

Cf. A187427.

Sequence in context: A126943 A209399 A192974 * A316878 A036368 A006071

Adjacent sequences:  A187425 A187426 A187427 * A187429 A187430 A187431

KEYWORD

nonn

AUTHOR

Michael Somos, Mar 09 2011

STATUS

approved

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Last modified June 19 02:58 EDT 2021. Contains 345125 sequences. (Running on oeis4.)