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A160528

Coefficients in the expansion of C^4/B^5, in Watson's notation of page 118.

1, 5, 20, 65, 190, 506, 1265, 2986, 6745, 14645, 30767, 62745, 124706, 242110, 460337, 858673, 1574140, 2839862, 5048435, 8852562, 15327290, 26224173, 44372688, 74301095, 123200079, 202394897, 329596348, 532299955, 852914900, 1356426196, 2141819621

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OFFSET

0,2

LINKS

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

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

FORMULA

See Maple code in A160525 for formula.

G.f.: Product_{n>=1} (1 - x^(7*n))^4/(1 - x^n)^5. - Seiichi Manyama, Nov 06 2016

a(n) ~ exp(Pi*sqrt(62*n/21)) * sqrt(31) / (4*sqrt(3) * 7^(5/2) * n). - Vaclav Kotesovec, Nov 10 2017

EXAMPLE

G.f. = 1 + 5*x + 20*x^2 + 65*x^3 + 190*x^4 + 506*x^5 + 1265*x^6 + ...

G.f. = q^23 + 5*q^47 + 20*q^71 + 65*q^95 + 190*q^119 + 506*q^143 + 1265*q^167 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))^4 /(1 - x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

CROSSREFS

Cf. A002300, A160525, A160526, A160527.

Sequence in context: A285928 A160506 A277212 * A023004 A001873 A391791

Adjacent sequences: A160525 A160526 A160527 * A160529 A160530 A160531

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 13 2009

STATUS

approved

URL: https://oeis.org/A160528

⇱ A160528 - OEIS