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.
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
KEYWORD
nonn
AUTHOR
Michael Somos, Apr 17 2004
STATUS
approved