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A187652
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Alternated binomial cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).
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0
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1, 0, 10, 194, 5932, 237624, 11820780, 702992968, 48662470640, 3843811669088, 341207224961856, 33627579102171680, 3643463136559851440, 430456189350273371648, 55075003474909952394848, 7586546772496980353804704
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = sum((-1)^(n-k)binomial(n,k)s(2k,k)),k=0..n)
a(n) ~ c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), where w = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... and c = 0.11686978539934159049334861225275481804523808136863346883911376048... - Vaclav Kotesovec, Jul 05 2021
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MAPLE
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seq(sum((-1)^(n-k)*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[(-1)^(n - k)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((-1)^(n-k)*binomial(n, k)*abs(stirling1(2*k, k)), k, 0, n), n, 0, 12);
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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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