A002868 Largest number in n-th row of triangle of Lah numbers (A008297 and A271703).

1, 1, 2, 6, 36, 240, 1800, 15120, 141120, 1693440, 21772800, 299376000, 4390848000, 68497228800, 1133317785600, 19833061248000, 396661224960000, 8299373322240000, 181400588328960000, 4135933413900288000, 98228418580131840000, 2426819753156198400000

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

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• 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

Essentially the same as A001286.

Cf. A000262, A008297, A105278, A271703.

Programs

Haskell

a002868 n = if n == 0 then 1 else maximum $ map abs $ a008297_row n
-- Reinhard Zumkeller, Sep 30 2014

Maple

with(combinat): for n from 0 to 35 do big := 1: for m from 1 to n do if big < n!*binomial(n-1,m-1)/m! then big := n!*binomial(n-1,m-1)/m! fi: od: printf(`%d,`,big): od:

Mathematica

a[n_] := ( big = 1; For[ m = 1 , m <= n, m++, b = n!*Binomial[n - 1, m - 1]/m!; If[ big < b , big = b ]]; big); Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Sep 21 2012, after Maple *)

Formula

For 2 <= n <= 7, equals (n+1)!*n/2. - Alexander R. Povolotsky, Oct 16 2006

Extensions

More terms from James Sellers, Jan 03 2001