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

Offset

1,3

References

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).

Links

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]

Gábor Czédli, Four-generated direct powers of partition lattices and authentication, arXiv:2004.14509 [math.RA], 2020. See Tables 3.3 to 3.8 pp. 7-8.

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A129084 A287892 A343278 * A096579 A350650 A120540

Adjacent sequences: A002867 A002868 A002869 * A002871 A002872 A002873

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jul 10 2000

Status

approved