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A187661
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Binomial convolution of the (signless) central Stirling numbers of the first kind and the central Stirling numbers of the second kind.
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2
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1, 2, 20, 369, 10192, 379850, 17930697, 1027046517, 69216504576, 5363945384274, 469658243947850, 45827641349686636, 4928867833029014503, 579101340954599901152, 73778702335232336908585, 10129059530832922239925140
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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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a(n) = Sum_{k=0..n} binomial(n,k) * s(2*k,k) * S(2*n-2*k,n-k).
a(n) ~ m * n^n * c^(2*n) * 2^(3*n-1) / (sqrt(Pi*(c-1)*n) * exp(n) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2) = 1.75643120862616967698..., and m = Sum_{j>=0} StirlingS2(2*j,j) * (2*c-1)^j / (j! * 2^(3*j) * c^(2*j)) = 1.170003674502655133465266152119563086693466... . - Vaclav Kotesovec, May 22 2014
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MAPLE
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seq(sum(binomial(n, k) * abs(combinat[stirling1](2*k, k)) * combinat[stirling2](2*(n-k), n-k), k=0..n), n=0..12);
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MATHEMATICA
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Table[Sum[Binomial[n, k]Abs[StirlingS1[2k, k]]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 15}]
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PROG
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(Maxima) makelist(sum(binomial(n, k)*abs(stirling1(2*k, k))*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);
(PARI) a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(2*k, k, 1)*stirling(2*(n-k), n-k, 2))); \\ Michel Marcus, May 28 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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