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A160462 Coefficients in the expansion of C^2/B^3, in Watson's notation of page 106. 7

%I

%S 1,3,9,22,51,106,215,411,766,1377,2423,4154,7001,11567,18834,30195,

%T 47809,74735,115585,176847,268064,402598,599695,886116,1299808,

%U 1893115,2739248,3938491,5629407,8000431,11309295,15904003,22256183,30998479,42981170,59337604

%N Coefficients in the expansion of C^2/B^3, in Watson's notation of page 106.

%H Seiichi Manyama, <a href="/A160462/b160462.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(13/15) * exp(Pi*sqrt(26*n/15)) / (20*n). - _Vaclav Kotesovec_, Nov 28 2016

%e x^7+3*x^31+9*x^55+22*x^79+51*x^103+106*x^127+215*x^151+...

%t nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^2/(1 - x^k)^3, {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), this sequence (k=2), A160463 (k=3), A160506 (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

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)