cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A002870 M2690 N1077 #46 Jul 02 2025 16:01:54
%S A002870 1,1,3,7,25,90,350,1701,7770,42525,246730,1379400,9321312,63436373,
%T A002870 420693273,3281882604,25708104786,197462483400,1709751003480,
%U A002870 15170932662679,132511015347084,1241963303533920,12320068811796900,120622574326072500,1203163392175387500
%N A002870 Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).
%D A002870 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002870 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002870 T. D. Noe, <a href="/A002870/b002870.txt">Table of n, a(n) for n=1..100</a>
%H A002870 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 A002870 Gábor Czédli, <a href="https://arxiv.org/abs/2004.14509">Four-generated direct powers of partition lattices and authentication</a>, arXiv:2004.14509 [math.RA], 2020. See Tables 3.3 to 3.8 pp. 7-8.
%H A002870 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 A002870 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 A002870 OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>
%t A002870 a[n_] := Max[ Table[ StirlingS2[n, k], {k, 1, n}]]; Table[a[n], {n, 1, 23}] (* _Jean-François Alcover_, Nov 15 2011 *)
%o A002870 (PARI) a(n) = vecmax(vector(n, k, stirling(n, k, 2))); \\ _Michel Marcus_, Oct 14 2015
%Y A002870 Cf. A008277 (triangle of Stirling numbers of the second kind), A024417 (k at which the maximum occurs).
%Y A002870 Cf. A065048.
%K A002870 nonn,nice,easy
%O A002870 1,3
%A A002870 _N. J. A. Sloane_
%E A002870 More terms from _James Sellers_, Jul 10 2000