A002868 Largest number in n-th row of triangle of Lah numbers (A008297 and A271703). (Formerly M1703 N0673)

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

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

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

Formula

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

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 *)

Prog

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

Crossrefs

Essentially the same as A001286.

Cf. A000262, A008297, A105278, A271703.

Sequence in context: A086325 A343581 A074424 * A002869 A293120 A052845

Adjacent sequences: A002865 A002866 A002867 * A002869 A002870 A002871

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jan 03 2001

Status

approved