A160526 Coefficients in the expansion of C^2/B^3, in Watson's notation of page 118.

1, 3, 9, 22, 51, 108, 221, 427, 804, 1461, 2596, 4497, 7652, 12767, 20984, 33958, 54255, 85580, 133520, 206066, 315010, 477083, 716494, 1067316, 1578102, 2316569, 3377965, 4894045, 7047970, 10091120, 14369439, 20354090, 28687663, 40239129, 56183879

Offset: 0

Author

N. J. A. Sloane, Nov 13 2009

Keywords

• nonn

Examples

			G.f. = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 108*x^5 + 221*x^6 + ...
G.f. = q^11 + 3*q^35 + 9*q^59 + 22*q^83 + 51*q^107 + 108*q^131 + 221*q^155 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

Crossrefs

Cf. A160525, A160527, A160528.

Programs

Mathematica

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 *)

Formula

See Maple code in A160525 for formula.

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

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