A160460 Coefficients in the expansion of C^6 / B^7, in Watson's notation of page 106.

1, 7, 35, 140, 490, 1541, 4480, 12195, 31465, 77525, 183626, 420077, 932030, 2011905, 4237130, 8725671, 17605602, 34861815, 67848095, 129946805, 245203642, 456303872, 838178470, 1520969100, 2728472695, 4841909821, 8504898720, 14794863270, 25500965320

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(29/15) * exp(Pi*sqrt(58*n/15)) / (500*n). - Vaclav Kotesovec, Nov 28 2016

Example

x^23 + 7*x^47 + 35*x^71 + 140*x^95 + 490*x^119 + 1541*x^143 + ...

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^6/(1 - x^k)^7, {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), this sequence (k=6), A160521 (k=7), A278555 (k=12), A278556 (k=18), A278557 (k=24), A278558 (k=30).

Sequence in context: A344101 A001941 A320050 * A160539 A023006 A001875

Adjacent sequences: A160457 A160458 A160459 * A160461 A160462 A160463

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2009

Status

approved