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Coefficients in the expansion of C^2/B^3, in Watson's notation of page 118.
4

%I #18 Sep 24 2019 02:21:55

%S 1,3,9,22,51,108,221,427,804,1461,2596,4497,7652,12767,20984,33958,

%T 54255,85580,133520,206066,315010,477083,716494,1067316,1578102,

%U 2316569,3377965,4894045,7047970,10091120,14369439,20354090,28687663,40239129,56183879

%N Coefficients in the expansion of C^2/B^3, in Watson's notation of page 118.

%H Seiichi Manyama, <a href="/A160526/b160526.txt">Table of n, a(n) for n = 0..1000</a>

%H G. N. Watson, <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

%F See Maple code in A160525 for formula.

%F G.f.: Product_{n>=1} (1 - x^(7*n))^2/(1 - x^n)^3. - _Seiichi Manyama_, Nov 06 2016

%F a(n) ~ exp(Pi*sqrt(38*n/21)) * sqrt(19) / (4*sqrt(3) * 7^(3/2) * n). - _Vaclav Kotesovec_, Nov 10 2017

%e G.f. = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 108*x^5 + 221*x^6 + ...

%e G.f. = q^11 + 3*q^35 + 9*q^59 + 22*q^83 + 51*q^107 + 108*q^131 + 221*q^155 + ...

%t nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))^2 /(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)

%Y Cf. A160525, A160527, A160528.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 13 2009