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%I #28 Nov 28 2016 05:53:43
%S 1,19,209,1710,11495,66862,347339,1645875,7221520,29668595,115116233,
%T 424720338,1498263563,5076482415,16583497160,52399330389,160586833362,
%U 478482249548,1388989067820,3935549005725,10901608510397,29565343541110,78604103339462
%N Expansion of Product_{n>=1} (1 - x^(5*n))^18/(1 - x^n)^19 in powers of x.
%H Seiichi Manyama, <a href="/A278556/b278556.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(5*n))^18/(1 - x^n)^19.
%F A278559(n) = 5^2*63*A160460(n) + 5^5*52*A278555(n-1) + 5^7*63*a(n-2) + 5^10*6*A278557(n-3) + 5^12*A278558(n-4) for n >= 4.
%F a(n) ~ sqrt(77/15) * exp(Pi*sqrt(154*n/15)) / (7812500*n). - _Vaclav Kotesovec_, Nov 28 2016
%t CoefficientList[ Series[ Product[(1 - x^(5n))^18/(1 - x^n)^19, {n, 22}], {x, 0, 22}], x] (* _Robert G. Wilson v_, Nov 24 2016 *)
%Y Cf. Product_{n>=1} (1 - x^(5*n))^k/(1 - x^n)^(k + 1): A160461 (k=1), A160462 (k=2), A160463 (k=3), A160506 (k=4), A071734 (k=5), A160460 (k=6), A160521 (k=7), A278555 (k=12), this sequence (k=18), A278557 (k=24), A278558 (k=30).
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 23 2016