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

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Crossrefs

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

Cf. A065048.

Programs

Mathematica

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

PARI

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

Extensions

More terms from James Sellers, Jul 10 2000