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A329806
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Expansion of Product_{k>=1} 1 / (1 - 6*x^k + x^(2*k))^(1/2).
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0
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1, 3, 16, 75, 385, 1971, 10473, 56139, 305394, 1674198, 9245506, 51325206, 286210243, 1601822505, 8992732043, 50619114252, 285583525237, 1614439389711, 9142794839933, 51858472602546, 294559269778199, 1675240507900632, 9538522900076376, 54367531265208579, 310179797595736539
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: exp(Sum_{k>=1} ( Sum_{d|k} d * (6 - x^d)^(k/d) ) * x^k / (2*k)).
G.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = g.f. of A001850 (central Delannoy numbers).
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
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MATHEMATICA
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nmax = 24; CoefficientList[Series[Product[1/(1 - 6 x^k + x^(2 k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x]
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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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