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%I #42 Sep 24 2019 02:32:03
%S 0,1,5,20,70,221,646,1772,4614,11490,27537,63808,143514,314279,671872,
%T 1405260,2881030,5799093,11476452,22357584,42922558,81284699,
%U 151974124,280739800,512761178,926568075,1657448779,2936506316,5155349836,8972488674,15487146900
%N Omit first term from A160539 and divide by 7.
%C These are Watson's coefficients beta'_n on page 125.
%H Seiichi Manyama, <a href="/A160549/b160549.txt">Table of n, a(n) for n = 0..1000</a>
%H G. N. Watson, <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128; see p. 125.
%F From _Seiichi Manyama_, Nov 07 2016: (Start)
%F a(n) = A160539(n)/7, n > 0.
%F G.f.: ((Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^7) - 1)/7. (End)
%F a(n) ~ 2^(5/4) * exp(4*Pi*sqrt(2*n/7)) / (7^(13/4) * n^(9/4)). - _Vaclav Kotesovec_, Nov 10 2016
%e G.f. = x + 5*x^2 + 20*x^3 + 70*x^4 + 221*x^5 + 646*x^6 + ...
%t 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 *)
%o (PARI) x='x+O('x^66); concat([0],Vec(eta(x^7)/eta(x)^7-1)/7) \\ _Joerg Arndt_, Nov 27 2016
%Y Cf. A160539.
%Y 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).
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 14 2009
%E Typo in definition corrected by _Seiichi Manyama_, Nov 07 2016
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