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A222058 Harmonic-geometric numbers. 6
0, 1, 4, 21, 138, 1095, 10208, 109473, 1328470, 18003675, 269580492, 4420677525, 78801184322, 1517300654415, 31386251780536, 694190761402377, 16348768018619694, 408472183061464515, 10791720442056792740, 300605598797790229629, 8805117712245004098586, 270562051319419652165175, 8702576800277309526639504, 292425620801795849417200881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.

FORMULA

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

E.g.f.: -log(2 - exp(x))/(2 - exp(x)). - Ilya Gutkovskiy, May 31 2018

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

MATHEMATICA

Table[Sum[StirlingS2[n, k]*Abs[StirlingS1[k + 1, 2]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 09 2013 *)

CROSSREFS

Row sums of A222057 or A222060.

Cf. A000254.

Sequence in context: A265952 A121124 A180399 * A265174 A087761 A245503

Adjacent sequences:  A222055 A222056 A222057 * A222059 A222060 A222061

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 08 2013

STATUS

approved

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Last modified October 21 01:31 EDT 2021. Contains 348128 sequences. (Running on oeis4.)