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%I #15 Jan 04 2019 04:18:54
%S 1,8,44,192,726,2457,7648,22220,60993,159478,399906,966600,2261630,
%T 5139897,11378988,24598683,52033372,107890610,219630050,439535138,
%U 865784403,1680352500,3216454360,6077280123,11343018559,20928404349,38194869384,68989715838
%N Coefficients in the expansion of C^7/B^8, in Watson's notation of page 106.
%H Seiichi Manyama, <a href="/A160521/b160521.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(11) * exp(Pi*sqrt(22*n/5)) / (2500*n). - _Vaclav Kotesovec_, Nov 28 2016
%e x^27+8*x^51+44*x^75+192*x^99+726*x^123+2457*x^147+7648*x^171+...
%t 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 *)
%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), A160460 (k=6), this sequence (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
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