A384470 a(n) = n! * Sum_{k=0..n} Stirling2(2*k,k) * Stirling2(2*n-2*k,n-k) / binomial(n,k).
1, 2, 29, 1108, 82924, 10302768, 1917699552, 499332175200, 173242955039616, 77238974345915520, 43027312823342164800, 29285800226400628915200, 23913110797474508388449280, 23071378298963178620672409600, 25964692904608781751347296204800, 33711625062334209438536728660070400
Offset: 0
Keywords
Programs
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Mathematica
Table[n! * Sum[StirlingS2[2*k, k] * StirlingS2[2*n-2*k, n-k] / Binomial[n, k], {k, 0, n}], {n, 0, 20}]
Formula
a(n) ~ 2^(2*n+1) * n^(2*n) / (sqrt(1-w) * exp(2*n) * (2-w)^n * w^n), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599...