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

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, A058583.

A000670 gives sum of terms in n-th row.

Sequence in context: A343581 A074424 A002868 * A293120 A052845 A052832

Adjacent sequences: A002866 A002867 A002868 * A002870 A002871 A002872

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved