A160533 Coefficients in the expansion of C^5/B^6, in Watson's notation of page 118.

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

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.

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

Cf. A160525, A160526, A160527, A160528.

Sequence in context: A160507 A182821 A277283 * A023005 A001874 A009061

Adjacent sequences: A160530 A160531 A160532 * A160534 A160535 A160536

Keyword

nonn

Author

N. J. A. Sloane, Nov 14 2009

Status

approved