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

Author

N. J. A. Sloane, Nov 14 2009

Keywords

• nonn

Comments

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

Examples

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

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.

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).

Programs

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 *)

PARI

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

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

Extensions

Typo in definition corrected by Seiichi Manyama, Nov 07 2016