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A095846 Expansion of eta(q^2)eta(q^10)^3/(eta(q^5)eta(q)^3) in powers of q. 2
1, 3, 8, 19, 41, 84, 164, 307, 557, 983, 1692, 2852, 4718, 7672, 12288, 19411, 30274, 46671, 71180, 107479, 160792, 238476, 350828, 512196, 742441, 1068914, 1529120, 2174216, 3073670, 4321444, 6044072, 8411283, 11649936, 16062102, 22048604 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=-u^2+v+6uv+4v^2+20uv^2.

Euler transform of period 10 sequence [3,2,3,2,4,2,3,2,3,0,...].

LINKS

Table of n, a(n) for n=1..35.

Kevin Acres, David Broadhurst, Eta quotients and Rademacher sums, arXiv:1810.07478 [math.NT], 2018. See Table 1 p. 10.

Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], 2015-2016.

FORMULA

G.f.: x*(Product_{k>0} (1-x^(2k))(1-x^(10k))^3/((1-x^k)^3(1-x^(5k)))).

a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(11/4) * 5^(5/4) * n^(3/4)). - Vaclav Kotesovec, Oct 13 2015

MATHEMATICA

nmax=60; Rest[CoefficientList[Series[x*Product[(1+x^k) * (1-x^(5*k))^2 * (1+x^(5*k))^3 / (1-x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Oct 13 2015 *)

PROG

(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff(eta(x^2+A)*eta(x^10+A)^3/(eta(x+A)^3*eta(x^5+A)), n))

CROSSREFS

Sequence in context: A006380 A260547 A182818 * A153732 A089924 A293947

Adjacent sequences:  A095843 A095844 A095845 * A095847 A095848 A095849

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 08 2004

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)