login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002870 Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).
(Formerly M2690 N1077)
5
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)
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: A148739 A129084 A287892 * A096579 A120540 A176829

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 11 11:03 EDT 2020. Contains 335626 sequences. (Running on oeis4.)