OFFSET
0,2
COMMENTS
In general, if m >= 1 and g.f. = Product_{k>=1} (1 - x^(7*k))^m / (1 - x^k)^(m+1), then a(n) ~ exp(Pi*sqrt((2*(6*m+7)*n)/21)) * sqrt(6*m+7)) / (4*sqrt(3) * 7^((m+1)/2) * n). - Vaclav Kotesovec, Nov 10 2017
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: Product_{n>=1} (1 - x^(7*n))^56/(1 - x^n)^57.
a(n) ~ exp(Pi*sqrt(686*n/21)) * sqrt(343) / (4*sqrt(3) * 7^(57/2) * n). - Vaclav Kotesovec, Nov 10 2017
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^56/(1 - x^k)^57, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^56/(1 - x^j)^57)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^56/(1 - x^j)^57: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^56/(1 - x^j)^57 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 24 2017
STATUS
approved