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

1, 3, 9, 22, 51, 106, 215, 411, 766, 1377, 2423, 4154, 7001, 11567, 18834, 30195, 47809, 74735, 115585, 176847, 268064, 402598, 599695, 886116, 1299808, 1893115, 2739248, 3938491, 5629407, 8000431, 11309295, 15904003, 22256183, 30998479, 42981170, 59337604

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Watson, G. N., Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

Formula

See Maple code in A160458 for formula.

a(n) ~ sqrt(13/15) * exp(Pi*sqrt(26*n/15)) / (20*n). - Vaclav Kotesovec, Nov 28 2016

Example

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

Mathematica

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 *)

Crossrefs

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).

Sequence in context: A034505 A143099 A365664 * A000711 A278668 A365665

Adjacent sequences: A160459 A160460 A160461 * A160463 A160464 A160465

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2009

Status

approved