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Expansion of Product_{k>=1} 1 / (1 - 6*x^k + x^(2*k))^(1/2).
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%I #5 Nov 21 2019 18:10:05

%S 1,3,16,75,385,1971,10473,56139,305394,1674198,9245506,51325206,

%T 286210243,1601822505,8992732043,50619114252,285583525237,

%U 1614439389711,9142794839933,51858472602546,294559269778199,1675240507900632,9538522900076376,54367531265208579,310179797595736539

%N Expansion of Product_{k>=1} 1 / (1 - 6*x^k + x^(2*k))^(1/2).

%F G.f.: exp(Sum_{k>=1} ( Sum_{d|k} d * (6 - x^d)^(k/d) ) * x^k / (2*k)).

%F G.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = g.f. of A001850 (central Delannoy numbers).

%F a(n) ~ sqrt(2) * (1 + sqrt(2))^(2*n - 1/2) / (c * sqrt(Pi*n)), where c = QPochhammer[1/(1 + sqrt(2))^2] = 0.799142925985081767883272500537236047... - _Vaclav Kotesovec_, Nov 21 2019

%t nmax = 24; CoefficientList[Series[Product[1/(1 - 6 x^k + x^(2 k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 24; CoefficientList[Series[Exp[Sum[Sum[d (6 - x^d)^(k/d), {d, Divisors[k]}] x^k/(2 k), {k, 1, nmax}]], {x, 0, nmax}], x]

%Y Cf. A001850, A067855.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Nov 21 2019