A282923 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A282923

Expansion of Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21 in powers of x.

1, 21, 252, 2233, 16170, 100926, 560945, 2837398, 13265679, 57989435, 239125579, 936702879, 3505361650, 12590400326, 43572202835, 145770820937, 472764167939, 1490002933265, 4573182416677, 13694526423445, 40076281579264, 114782535792335, 322167257486123, 887188897987819, 2399619923361150, 6380874322337452, 16695968482412345

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21.

a(n) ~ exp(Pi*sqrt(254*n/21)) * sqrt(127) / (4*sqrt(3) * 7^(21/2) * n). - Vaclav Kotesovec, Nov 10 2017

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^20/(1 - x^k)^21, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

PROG

(PARI) my(x='x+O('x^30)); Vec(prod(j=1, 30, (1 - x^(7*j))^20/(1 - x^j)^21)) \\ G. C. Greubel, Nov 18 2018

(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^20/(1 - x^j)^21: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018

(Sage)

R = PowerSeriesRing(ZZ, 'x')

prec = 30

x = R.gen().O(prec)

s = prod((1 - x^(7*j))^20/(1 - x^j)^21 for j in (1..prec))

print(s.coefficients()) # G. C. Greubel, Nov 18 2018

CROSSREFS

Cf. A282919.

Sequence in context: A165095 A165099 A165108 * A023019 A036220 A022649

Adjacent sequences: A282920 A282921 A282922 * A282924 A282925 A282926

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 24 2017

STATUS

approved