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%I #26 Nov 27 2016 07:26:40
%S 0,1,7,38,175,714,2653,9139,29563,90650,265401,746142,2023566,5314008,
%T 13554912,33673525,81654104,193646588,449903128,1025532912,2296519589,
%U 5058078488,10968488747,23440057192,49406752403,102792264765,211242738976,429066735314,861868377262,1713014236294,3370525567099
%N Expansion of ((Product_{n>=1} (1 - x^(11*n))/(1 - x^n)^11) - 1)/11 in powers of x.
%H Seiichi Manyama, <a href="/A277912/b277912.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: ((Product_{n>=1} (1 - x^(11*n))/(1 - x^n)^11) - 1)/11.
%F a(n) ~ 5^(11/4) * exp(4*Pi*sqrt(5*n/11)) / (sqrt(2)*11^(17/4)*n^(13/4)). - _Vaclav Kotesovec_, Nov 10 2016
%e G.f. = x + 7*x^2 + 38*x^3 + 175*x^4 + 714*x^5 + 2653*x^6 + ...
%t nmax = 50; CoefficientList[Series[(Product[(1 - x^(11*j))/(1 - x^j)^11, {j, 1, nmax}] - 1)/11, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2016 *)
%t a[ n_] := SeriesCoefficient[ (QPochhammer[ x^11] / QPochhammer[ x]^11 - 1) / 11, {x, 0, n}]; (* _Michael Somos_, Nov 13 2016 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^11 + A) / eta(x + A)^11 - 1) / 11, n))}; /* _Michael Somos_, Nov 13 2016 */
%o (PARI) x='x+O('x^66); concat([0],Vec(eta(x^11)/eta(x)^11-1)/11) \\ _Joerg Arndt_, Nov 27 2016
%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), A160549 (k=7), this sequence (k=11).
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 07 2016
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