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A187654
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Binomial cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).
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1
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1, 2, 14, 262, 7740, 305536, 15061692, 890220752, 61347750704, 4829414749504, 427559293150976, 42047904926171552, 4547772798257998256, 536504774914535869664, 68557641564333466819744, 9433619169586732241895776
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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(2k,k).
a(n) ~ exp((2*c-1)/(8*c^2)) * abs(Stirling1(2*n,n)) ~ 2^(3*n-1) * n^n * exp((2*c-1)/(8*c^2)-n) * c^(2*n) / (sqrt(Pi*n*(c-1)) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... - Vaclav Kotesovec, May 21 2014
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MAPLE
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seq(sum(binomial(n, k)*abs(combinat[stirling1](2*k, 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]], {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)), k, 0, n), n, 0, 12);
(PARI) a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(2*k, k, 1))); \\ Michel Marcus, Aug 03 2021
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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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