A190187 Denominator of expression W_n occurring in analysis of bubble sort.

1, 1, 3, 6, 15, 90, 630, 720, 45360, 64800, 4989600, 59875200, 778377600, 1556755200, 163459296000, 373621248000, 44460928512000, 800296713216000, 15205637551104000, 3949516247040000, 6386367771463680000, 20071441567457280000, 3231502092360622080000, 5965850016665763840000, 1938901255416373248000000, 7201633234403672064000000

Offset

1,3

References

D. E. Knuth, The Art of Computer Programming, Vol. 3, Section 5.2.2, p. 129.

Links

G. C. Greubel, Table of n, a(n) for n = 1..450

Formula

W_n = Sum_{r=0..(n-1)}( Sum_{s=(r+1)..n} s!*r^(n-s) )/n!.

W_n = denominator(A190194(n)/n!).

Example

1, 2, 10/3, 29/6, 97/15, 739/90, 6331/630, 8617/720, 633127/45360, 1037497/64800, ...

Maple

W:=proc(n) local t1, r, s;
t1:=add( add(s!*r^(n-s), s=r+1..n), r=0..n-1);
t1/n!;
end;

Mathematica

Denominator[Table[n! + Sum[ Sum[s!*k^(n - s), {s, k + 1, n}], {k, 1, n - 1}]/n!, {n, 1, 50}]] (* G. C. Greubel, Dec 28 2017 *)

Prog

(PARI) for(n=1, 30, print1(denominator(1 + sum(k=1, n-1, sum(s=k+1, n, s!*k^(n-s)))/n!), ", ")) \\ G. C. Greubel, Dec 28 2017

Crossrefs

Cf. A190186.

Sequence in context: A009192 A013273 A013277 * A144549 A280992 A013270

Adjacent sequences: A190184 A190185 A190186 * A190188 A190189 A190190

Keyword

nonn,frac

Author

N. J. A. Sloane, May 05 2011

Status

approved