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A002870 Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).
(Formerly M2690 N1077)
1, 1, 3, 7, 25, 90, 350, 1701, 7770, 42525, 246730, 1379400, 9321312, 63436373, 420693273, 3281882604, 25708104786, 197462483400, 1709751003480, 15170932662679, 132511015347084, 1241963303533920, 12320068811796900, 120622574326072500, 1203163392175387500 (list; graph; refs; listen; history; text; internal format)



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

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


T. D. Noe, Table of n, a(n) for n=1..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 835. [scanned copy]

Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.

T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]

OEIS Wiki, Sorting numbers


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


(PARI) a(n) = vecmax(vector(n, k, stirling(n, k, 2))); \\ Michel Marcus, Oct 14 2015


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

Sequence in context: A148739 A129084 A287892 * A096579 A120540 A176829

Adjacent sequences:  A002867 A002868 A002869 * A002871 A002872 A002873




N. J. A. Sloane


More terms from James A. Sellers, Jul 10 2000



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Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)