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 A190187 Denominator of expression W_n occurring in analysis of bubble sort. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 28 19:19 EDT 2023. Contains 365737 sequences. (Running on oeis4.)