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A160526 Coefficients in the expansion of C^2/B^3, in Watson's notation of page 118. 4
1, 3, 9, 22, 51, 108, 221, 427, 804, 1461, 2596, 4497, 7652, 12767, 20984, 33958, 54255, 85580, 133520, 206066, 315010, 477083, 716494, 1067316, 1578102, 2316569, 3377965, 4894045, 7047970, 10091120, 14369439, 20354090, 28687663, 40239129, 56183879 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

G. N. Watson, Ramanujans Vermutung √ľber Zerf√§llungsanzahlen, 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))^2/(1 - x^n)^3. - Seiichi Manyama, Nov 06 2016

a(n) ~ exp(Pi*sqrt(38*n/21)) * sqrt(19) / (4*sqrt(3) * 7^(3/2) * n). - Vaclav Kotesovec, Nov 10 2017

EXAMPLE

G.f. = 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 108*x^5 + 221*x^6 + ...

G.f. = q^11 + 3*q^35 + 9*q^59 + 22*q^83 + 51*q^107 + 108*q^131 + 221*q^155 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))^2 /(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

CROSSREFS

Cf. A160525, A160527, A160528.

Sequence in context: A160462 A000711 A278668 * A121589 A227454 A000716

Adjacent sequences:  A160523 A160524 A160525 * A160527 A160528 A160529

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 13 2009

STATUS

approved

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Last modified June 5 09:55 EDT 2020. Contains 334830 sequences. (Running on oeis4.)