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A002869 Largest number in n-th row of triangle A019538.

%I A002869 M1704 N0674 #49 Oct 24 2024 12:33:42
%S A002869 1,1,2,6,36,240,1800,16800,191520,2328480,30240000,479001600,
%T A002869 8083152000,142702560000,2731586457600,59056027430400,
%U A002869 1320663933388800,30575780537702400,783699448602470400,21234672840116736000,591499300737945600000
%N A002869 Largest number in n-th row of triangle A019538.
%D A002869 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002869 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002869 Danny Rorabaugh, <a href="/A002869/b002869.txt">Table of n, a(n) for n = 0..400</a> (first 251 terms from Reinhard Zumkeller)
%H A002869 Jens Gulin and Kalle Åström, <a href="https://lucris.lub.lu.se/ws/portalfiles/portal/196591300/IPINwip_ARMPIT_final.pdf">Alternative implementations of the Auxiliary Duplicating Permutation Invariant Training</a>, Proc Work-in-Progress Papers at 14th Int'l Conf. Indoor Positioning Indoor Nav. (IPIN-WiP 2024). See p. 6.
%H A002869 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 A002869 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 A002869 OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>
%p A002869 f := proc(n) local t1, k; t1 := 0; for k to n do if t1 < A019538(n, k) then t1 := A019538(n, k) fi; od; t1; end;
%t A002869 A019538[n_, k_] := k!*StirlingS2[n, k]; f[0] = 1; f[n_] := Module[{t1, k}, t1 = 0; For[k = 1, k <= n, k++, If[t1 < A019538[n, k], t1 = A019538[n, k]]]; t1]; Table[f[n], {n, 0, 20}] (* _Jean-François Alcover_, Dec 26 2013, after Maple *)
%o A002869 (Haskell)
%o A002869 a002869 0 = 1
%o A002869 a002869 n = maximum $ a019538_row n
%o A002869 -- _Reinhard Zumkeller_, Dec 15 2013
%o A002869 (Sage)
%o A002869 def A002869(n):
%o A002869     return max(factorial(k)*stirling_number2(n,k) for k in range(1,n+1))
%o A002869 [A002869(i) for i in range(1, 20)] # _Danny Rorabaugh_, Oct 10 2015
%Y A002869 Cf. A019538, A131689, A058583.
%Y A002869 A000670 gives sum of terms in n-th row.
%K A002869 nonn,nice,easy
%O A002869 0,3
%A A002869 _N. J. A. Sloane_