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A160463 Coefficients in the expansion of C^3/B^4, in Watson's notation of page 106. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 12 10:20 EDT 2020. Contains 335657 sequences. (Running on oeis4.)