A160549 Omit first term from A160539 and divide by 7.

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

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 über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128; see p. 125.

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