login
A160460
Coefficients in the expansion of C^6 / B^7, in Watson's notation of page 106.
11
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 13 2009
STATUS
approved