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

Author

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

Keywords

• nonn
• nice

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.

Examples

			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.
		

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.

Crossrefs

Cf. A000124, A107868, A129933.

Cf. A000142.

Programs

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

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 *)

Formula

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

Extensions

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