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

Author

N. J. A. Sloane, May 05 2011

Keywords

• nonn
• frac

Examples

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

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

Crossrefs

Cf. A190186.

Programs

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 *)

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

Formula

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

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