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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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)
• Jens Gulin and Kalle Åström, Alternative implementations of the Auxiliary Duplicating Permutation Invariant Training, Proc Work-in-Progress Papers at 14th Int'l Conf. Indoor Positioning Indoor Nav. (IPIN-WiP 2024). See p. 6.
• 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

Crossrefs

Cf. A019538, A131689, A058583.

A000670 gives sum of terms in n-th row.

Programs

Haskell

a002869 0 = 1
a002869 n = maximum $ a019538_row n
-- Reinhard Zumkeller, Dec 15 2013

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 *)

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