A093830 Expansion of q^(-1/2)(eta(q^2)eta(q^10)/(eta(q)eta(q^5)))^2 in powers of q.

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

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: A275548 A260710 A359994 * A320268 A118033 A048810

Adjacent sequences: A093827 A093828 A093829 * A093831 A093832 A093833

Keyword

nonn

Author

Michael Somos, Apr 17 2004

Status

approved