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A160533
Coefficients in the expansion of C^5/B^6, in Watson's notation of page 118.
1
1, 6, 27, 98, 315, 918, 2492, 6367, 15495, 36145, 81326, 177219, 375461, 775544, 1565870, 3096615, 6008917, 11458720, 21502964, 39754385, 72485518, 130464603, 231989748, 407847488, 709365160, 1221364655, 2082872680, 3519963776, 5897536697, 9800358525
OFFSET
0,2
LINKS
G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.
FORMULA
See Maple code in A160525 for formula.
G.f.: Product_{n>=1} (1 - x^(7*n))^5/(1 - x^n)^6. - Seiichi Manyama, Nov 06 2016
a(n) ~ exp(Pi*sqrt(74*n/21)) * sqrt(37) / (1372*sqrt(3)*n). - Vaclav Kotesovec, Nov 10 2017
EXAMPLE
G.f. = 1 + 6*x + 27*x^2 + 98*x^3 + 315*x^4 + 918*x^5 + 2492*x^6 + ...
G.f. = q^29 + 6*q^53 + 27*q^77 + 98*q^101 + 315*q^125 + 918*q^149 + 2492*q^173 + ...
MATHEMATICA
nn = 29; CoefficientList[Series[Product[(1 - x^(7 n))^5/(1 - x^n)^6, {n, nn}], {x, 0, nn}], x] (* Michael De Vlieger, Nov 06 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 14 2009
STATUS
approved