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A160549 Omit first term from A160539 and divide by 7. 6
0, 1, 5, 20, 70, 221, 646, 1772, 4614, 11490, 27537, 63808, 143514, 314279, 671872, 1405260, 2881030, 5799093, 11476452, 22357584, 42922558, 81284699, 151974124, 280739800, 512761178, 926568075, 1657448779, 2936506316, 5155349836, 8972488674, 15487146900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

These are Watson's coefficients beta'_n on page 125.

LINKS

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

G. N. Watson, Ramanujans Vermutung √ľber Zerf√§llungsanzahlen, J. ReineAngew.Math. (Crelle), 179 (1938), 97-128.

FORMULA

From Seiichi Manyama, Nov 07 2016: (Start)

a(n) = A160539(n)/7, n > 0.

G.f.: ((Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^7) - 1)/7. (End)

a(n) ~ 2^(5/4) * exp(4*Pi*sqrt(2*n/7)) / (7^(13/4) * n^(9/4)). - Vaclav Kotesovec, Nov 10 2016

EXAMPLE

G.f. = x + 5*x^2 + 20*x^3 + 70*x^4 + 221*x^5 + 646*x^6 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[(Product[(1 - x^(7*j))/(1 - x^j)^7, {j, 1, nmax}] - 1)/7, {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2016 *)

PROG

(PARI) x='x+O('x^66); concat([0], Vec(eta(x^7)/eta(x)^7-1)/7) \\ Joerg Arndt, Nov 27 2016

CROSSREFS

Cf. A160539.

Cf. Expansion of ((Product_{n>=1} (1 - x^(k*n))/(1 - x^n)^k) - 1)/k in powers of x: A014968 (k=2), A277968 (k=3), A277974 (k=5), this sequence (k=7), A277912 (k=11).

Sequence in context: A007327 A055403 A291288 * A089094 A080930 A169792

Adjacent sequences:  A160546 A160547 A160548 * A160550 A160551 A160552

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 14 2009

EXTENSIONS

Typo in definition corrected by Seiichi Manyama, Nov 07 2016

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)