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A093830 Expansion of q^(-1/2)(eta(q^2)eta(q^10)/(eta(q)eta(q^5)))^2 in powers of q. 0
1, 2, 3, 6, 9, 16, 26, 38, 58, 84, 124, 178, 249, 348, 478, 660, 896, 1202, 1610, 2132, 2822, 3706, 4827, 6270, 8093, 10420, 13346, 17008, 21608, 27332, 34490, 43350, 54286, 67806, 84404, 104828, 129810, 160274, 197440, 242584, 297429, 363802 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

G.f. A(x) satisfies 0=f(xA(x)^2,x^2A(x^2)^2) where f(u,v)=u^2-v-8uv-16uv^2.

LINKS

Table of n, a(n) for n=0..41.

FORMULA

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

a(n) ~ exp(2*Pi*sqrt(n/5)) / (8 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2015

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1/((1-x^(10*k-5)) * (1-x^(2*k-1)))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2015 *)

PROG

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

(PARI) a(n)=if(n<0, 0, polcoeff((1/prod(k=1, (n+5)\10, 1-x^(10*k-5), 1+x*O(x^n))/prod(k=1, (n+1)\2, 1-x^(2*k-1), 1+x*O(x^n)))^2, n))

CROSSREFS

Sequence in context: A301753 A275548 A260710 * A320268 A118033 A048810

Adjacent sequences:  A093827 A093828 A093829 * A093831 A093832 A093833

KEYWORD

nonn

AUTHOR

Michael Somos, Apr 17 2004

STATUS

approved

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Last modified September 30 22:26 EDT 2020. Contains 337440 sequences. (Running on oeis4.)