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 A002869 Largest number in n-th row of triangle A019538. (Formerly M1704 N0674) 4

%I M1704 N0674

%S 1,1,2,6,36,240,1800,16800,191520,2328480,30240000,479001600,

%T 8083152000,142702560000,2731586457600,59056027430400,

%U 1320663933388800,30575780537702400,783699448602470400,21234672840116736000,591499300737945600000

%N Largest number in n-th row of triangle A019538.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Reinhard Zumkeller and Danny Rorabaugh, <a href="/A002869/b002869.txt">Table of n, a(n) for n = 0..400</a> (first 251 terms from Reinhard Zumkeller)

%H 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 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 OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>

%p 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 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 0 = 1

%o a002869 n = maximum \$ a019538_row n

%o -- _Reinhard Zumkeller_, Dec 15 2013

%o (Sage) max([factorial(k)*stirling_number2(n,k) for k in range(1,n+1)]) # _Danny Rorabaugh_, Oct 10 2015

%Y Cf. A019538, A058583.

%Y A000670 gives sum of terms in n-th row.

%K nonn,nice,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)