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%I #22 Jan 04 2019 04:09:43
%S 1,7,35,140,490,1541,4480,12195,31465,77525,183626,420077,932030,
%T 2011905,4237130,8725671,17605602,34861815,67848095,129946805,
%U 245203642,456303872,838178470,1520969100,2728472695,4841909821,8504898720,14794863270,25500965320
%N Coefficients in the expansion of C^6 / B^7, in Watson's notation of page 106.
%H Seiichi Manyama, <a href="/A160460/b160460.txt">Table of n, a(n) for n = 0..1000</a>
%H Watson, G. N., <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung ueber Zerfaellungsanzahlen.</a> J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.
%F See Maple code in A160458 for formula.
%F a(n) ~ sqrt(29/15) * exp(Pi*sqrt(58*n/15)) / (500*n). - _Vaclav Kotesovec_, Nov 28 2016
%e x^23 + 7*x^47 + 35*x^71 + 140*x^95 + 490*x^119 + 1541*x^143 + ...
%t 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 *)
%Y 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).
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 13 2009