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Coefficients in the expansion of C^4/B^5, in Watson's notation of page 106.
7

%I #16 Jan 04 2019 04:17:49

%S 1,5,20,65,190,502,1245,2910,6505,13965,29005,58455,114810,220240,

%T 413775,762635,1381550,2463060,4327445,7500260,12836645,21712470,

%U 36323930,60143320,98620425,160238035,258110955,412367705,653709340,1028658150,1607306688

%N Coefficients in the expansion of C^4/B^5, in Watson's notation of page 106.

%H Seiichi Manyama, <a href="/A160506/b160506.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(7/5) * exp(Pi*sqrt(14*n/5)) / (100*n). - _Vaclav Kotesovec_, Nov 28 2016

%e x^15+5*x^39+20*x^63+65*x^87+190*x^111+502*x^135+1245*x^159+...

%t nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^4/(1 - x^k)^5, {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), this sequence (k=4), A071734 (k=5), A160460 (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