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A160506 Coefficients in the expansion of C^4/B^5, in Watson's notation of page 106. 7
1, 5, 20, 65, 190, 502, 1245, 2910, 6505, 13965, 29005, 58455, 114810, 220240, 413775, 762635, 1381550, 2463060, 4327445, 7500260, 12836645, 21712470, 36323930, 60143320, 98620425, 160238035, 258110955, 412367705, 653709340, 1028658150, 1607306688 (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(7/5) * exp(Pi*sqrt(14*n/5)) / (100*n). - Vaclav Kotesovec, Nov 28 2016

EXAMPLE

x^15+5*x^39+20*x^63+65*x^87+190*x^111+502*x^135+1245*x^159+...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^4/(1 - x^k)^5, {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), A160463 (k=3), this sequence (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: A001939 A100534 A285928 * A277212 A160528 A023004

Adjacent sequences:  A160503 A160504 A160505 * A160507 A160508 A160509

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 13 2009

STATUS

approved

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Last modified July 8 03:25 EDT 2020. Contains 335503 sequences. (Running on oeis4.)