A160521 Coefficients in the expansion of C^7/B^8, in Watson's notation of page 106.

1, 8, 44, 192, 726, 2457, 7648, 22220, 60993, 159478, 399906, 966600, 2261630, 5139897, 11378988, 24598683, 52033372, 107890610, 219630050, 439535138, 865784403, 1680352500, 3216454360, 6077280123, 11343018559, 20928404349, 38194869384, 68989715838

Offset

0,2

Links

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

Watson, G. N., Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

Formula

See Maple code in A160458 for formula.

a(n) ~ sqrt(11) * exp(Pi*sqrt(22*n/5)) / (2500*n). - Vaclav Kotesovec, Nov 28 2016

Example

x^27+8*x^51+44*x^75+192*x^99+726*x^123+2457*x^147+7648*x^171+...

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^7/(1 - x^k)^8, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 28 2016 *)

Crossrefs

Cf. Product_{n>=1} (1 - x^(5*n))^k/(1 - x^n)^(k + 1): A160461 (k=1), A160462 (k=2), A160463 (k=3), A160506 (k=4), A071734 (k=5), A160460 (k=6), this sequence (k=7), A278555 (k=12), A278556 (k=18), A278557 (k=24), A278558 (k=30).

Sequence in context: A181358 A005798 A092877 * A277958 A283077 A023007

Adjacent sequences: A160518 A160519 A160520 * A160522 A160523 A160524

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2009

Status

approved