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A160462 Coefficients in the expansion of C^2/B^3, in Watson's notation of page 106. 7
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 (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(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: A260545 A034505 A143099 * A000711 A278668 A160526

Adjacent sequences:  A160459 A160460 A160461 * A160463 A160464 A160465

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 13 2009

STATUS

approved

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Last modified July 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)