|
| |
|
|
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
|
|
|
|
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
|
|
|
|
STATUS
|
approved
|
| |
|
|
