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.

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

Author

Clark Kimberling

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A002870 (maximum values), A008277 (triangle of Stirling numbers of the second kind).

Programs

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 *)

Formula

a(n) ~ n/LambertW(n) - 1 (conjecture). - Mats Granvik, Oct 16 2013

Extensions

More terms retrieved from the b-file by R. J. Mathar, Sep 17 2008