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A002870 Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).
(Formerly M2690 N1077)
4

%I M2690 N1077

%S 1,1,3,7,25,90,350,1701,7770,42525,246730,1379400,9321312,63436373,

%T 420693273,3281882604,25708104786,197462483400,1709751003480,

%U 15170932662679,132511015347084,1241963303533920,12320068811796900,120622574326072500,1203163392175387500

%N Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002870/b002870.txt">Table of n, a(n) for n=1..100</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 835. [scanned copy]

%H Victor Meally, <a href="/A002868/a002868.pdf">Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.</a>

%H T. S. Motzkin, <a href="/A000262/a000262.pdf">Sorting numbers for cylinders and other classification numbers</a>, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]

%H OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>

%t a[n_] := Max[ Table[ StirlingS2[n, k], {k, 1, n}]]; Table[a[n], {n, 1, 23}] (* _Jean-Fran├žois Alcover_, Nov 15 2011 *)

%o (PARI) a(n) = vecmax(vector(n, k, stirling(n, k, 2))); \\ _Michel Marcus_, Oct 14 2015

%Y Cf. A008277 (triangle of Stirling numbers of the second kind), A024417 (k at which the maximum occurs).

%K nonn,nice,easy

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Jul 10 2000

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Last modified April 18 08:37 EDT 2019. Contains 322209 sequences. (Running on oeis4.)