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

Author

N. J. A. Sloane, Nov 13 2009

Keywords

• nonn

Examples

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

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.

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).

Programs

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 *)

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