VOOZH about

URL: https://oeis.org/A024417

⇱ A024417 - OEIS

login
A024417
s(n,a(n)) = max{s(n,k): k=1,2,...,n}, n >= 1, where s(n,k) = Stirling numbers of the second kind.
3
1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23
OFFSET
1,3
LINKS
L. H. Harper, Stirling Behavior is Asymptotically Normal, Ann. Math. Statist. 38(2) (1967), 410-414.
B. C. Rennie and A. J. Dobson, On stirling numbers of the second kind, Journal of Combinatorial Theory, vol. 7, iss. 2 (1969), 116-121.
FORMULA
a(n) ~ n/LambertW(n) - 1 (conjecture). - Mats Granvik, Oct 16 2013
a(n) ~ n/log(n) + O(n*sqrt(log log n)/(log n)^(3/2)). [Rennie & Dobson]
Granvik's conjecture follows from W(n) = log(n) - log(log(n)) + o(1). (See also saddle-point-based asymptotic (for rows' centres of mass rather than maximums) in A000110, which uses W directly.) - Natalia L. Skirrow, Nov 29 2025
MATHEMATICA
a[n_] := (m = Max[t = Table[ StirlingS2[n, k], {k, 1, n}]]; Position[t, m][[1, 1]]); Table[a[n], {n, 1, 77}] (* Jean-François Alcover, Nov 15 2011 *)
CROSSREFS
Cf. A002870 (maximum values), A008277 (triangle of Stirling numbers of the second kind).
Sequence in context: A030530 A084500 A084557 * A060021 A350029 A000006
KEYWORD
nonn
EXTENSIONS
More terms retrieved from the b-file by R. J. Mathar, Sep 17 2008
STATUS
approved