A129893 a(n) = s!/(s-n)! where s = (n*(n+1)/2)+1.

1, 2, 12, 210, 7920, 524160, 53721360, 7866331200, 1556675366400, 399790821830400, 129210868410624000, 51295616536721356800, 24529502681864788608000, 13903600298770901182464000

Offset

0,2

Comments

Bread Shop Open!. We have a loaf of bread which has a kernel of corns irregularly inside. We cut the loaf n times getting the maximal number (s, see A000124) of pieces and distribute one piece to each of n people. The remaining pieces of bread will be the prize for the winner. The sequence gives the number of cases when n pieces are distributed to n persons.

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.

H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 177.

N. Reading, On the structure of Bruhat Order, Ph.D. dissertation, University of Minnesota, anticipated 2002.

A. M. Robert, A Course in p-adic Analysis, Springer-Verlag, 2000; p. 213.

N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.

W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 30.

A. M. Yaglom and I. M. Yaglom: Challenging Mathematical Problems with Elementary Solutions. Vol. I. Combinatorial Analysis and Probability Theory. New York: Dover Publications, Inc., 1987, p. 13, #44 (First published: San Francisco: Holden-Day, Inc., 1964)

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..120

A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, arXiv:math/0112281 [math.CO], 2001; Annals. Combin., 7 (2003), 1-14; see Example 3.5.

L. Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 22.

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

D. A. Lind, On a class of nonlinear binomial sums, Fib. Quart., 3 (1965), 292-298.

D. J. Price, Some unusual series occurring in n-dimensional geometry, Math. Gaz., 30 (1946), 149-150.

R. Simion and F. W. Schmidt, Restricted permutations, European J. Combin., 6, 383-406, 1985.

Formula

a(n) = sPn, where s=(n*(n+1)/2)+1.

Example

a(2)=12 s=4,n=2 because we can write 12=4*3.
a(3)=210 s=7,n=3 because we can write 210=7*6*5.

Mathematica

Table[s=(n(n+1))/2+1; s!/(s-n)!, {n, 0, 20}] (* Harvey P. Dale, Nov 15 2012 *)
#[[1]]!/(#[[1]]-#[[2]])!&/@With[{nn=20}, Thread[{Accumulate[ Range[0, nn]]+ 1, Range[0, nn]}]] (* Harvey P. Dale, Sep 12 2015 *)

Prog

(Haskell)
a129893 n = a129893_list !! n
a129893_list = 1 : zipWith div (tail fs) fs where
   fs = map a000142 a000124_list
-- Reinhard Zumkeller, Oct 03 2012

Crossrefs

Cf. A000124, A107868, A129933.

Cf. A000142.

Sequence in context: A306715 A012598 A156489 * A008352 A082491 A292812

Adjacent sequences: A129890 A129891 A129892 * A129894 A129895 A129896

Keyword

nonn,nice

Author

Kim Dong Seok (Go Jae Song, Nam Dae Young) from KNU (gjs0419(AT)nate.com), Jun 04 2007

Extensions

Typo fixed in a(13) by Reinhard Zumkeller, Oct 03 2012

Status

approved