A160463 Coefficients in the expansion of C^3/B^4, in Watson's notation of page 106.

1, 4, 14, 40, 105, 249, 562, 1198, 2460, 4865, 9352, 17486, 31973, 57220, 100550, 173665, 295413, 495339, 819900, 1340655, 2167825, 3468579, 5495908, 8628080, 13428945, 20730689, 31757174, 48293585, 72933885, 109421095, 163135433, 241763735, 356246552

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(17/3) * exp(Pi*sqrt(34*n/15)) / (100*n). - Vaclav Kotesovec, Nov 28 2016

Example

x^11+4*x^35+14*x^59+40*x^83+105*x^107+249*x^131+562*x^155+...

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^3/(1 - x^k)^4, {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), A160462 (k=2), this sequence (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: A001938 A066368 A274327 * A278680 A121593 A160527

Adjacent sequences: A160460 A160461 A160462 * A160464 A160465 A160466

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2009

Status

approved