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A222058
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Harmonic-geometric numbers.
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7
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0, 1, 4, 21, 138, 1095, 10208, 109473, 1328470, 18003675, 269580492, 4420677525, 78801184322, 1517300654415, 31386251780536, 694190761402377, 16348768018619694, 408472183061464515, 10791720442056792740, 300605598797790229629, 8805117712245004098586, 270562051319419652165175, 8702576800277309526639504, 292425620801795849417200881
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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_{k=0..n} Stirling2(n,k)*|Stirling1(k+1,2)|.
Maximal term in the sum is asymptotically in position k = n/(2*log(2)) and limit n-> infinity (a(n)/n!)^(1/n) = 1/log(2). - Vaclav Kotesovec, Feb 09 2013
a(n) ~ n! * log(n) / (2 * (log(2))^(n+1)) * (1 + (gamma - log(2) - log(log(2))) / log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 13 2018
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MATHEMATICA
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Table[Sum[StirlingS2[n, k]*Abs[StirlingS1[k + 1, 2]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 09 2013 *)
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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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