A002869 - OEIS

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A002869

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

1, 1, 2, 6, 36, 240, 1800, 16800, 191520, 2328480, 30240000, 479001600, 8083152000, 142702560000, 2731586457600, 59056027430400, 1320663933388800, 30575780537702400, 783699448602470400, 21234672840116736000, 591499300737945600000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

Danny Rorabaugh, Table of n, a(n) for n = 0..400 (first 251 terms from Reinhard Zumkeller)

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

MAPLE

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;

MATHEMATICA

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 *)

PROG

(Haskell)

a002869 0 = 1

a002869 n = maximum $ a019538_row n

-- Reinhard Zumkeller, Dec 15 2013

(Sage)

def A002869(n):

return max(factorial(k)*stirling_number2(n, k) for k in range(1, n+1))

[A002869(i) for i in range(1, 20)] # Danny Rorabaugh, Oct 10 2015

CROSSREFS

Cf. A019538, A131689, A058583.

A000670 gives sum of terms in n-th row.