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 A190186 Numerator of expression W_n occurring in analysis of bubble sort. 7
 1, 2, 10, 29, 97, 739, 6331, 8617, 633127, 1037497, 90414391, 1214394319, 17506484887, 38519714137, 4419404086711, 10972377997177, 1410921315134167, 27316952872520239, 555986170009834231, 154130283599461067, 265123004099257677847, 883735015159907270617, 150492959376114678237751, 293138621437723505079883, 100289605416287509517021527 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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..445 FORMULA W_n = Sum_{r=0..(n-1)}( Sum_{s=(r+1)..n} s!*r^(n-s) )/n!. W_n = numerator(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 Numerator[Table[n! + Sum[ Sum[s!*k^(n - s), {s, k + 1, n}], {k, 1, n - 1}]/n!, {n, 1, 50}]] (* G. C. Greubel, Dec 29 2017 *) PROG (PARI) for(n=1, 30, print1(numerator(1 + sum(k=1, n-1, sum(s=k+1, n, s!*k^(n-s)))/n!), ", ")) \\ G. C. Greubel, Dec 29 2017 CROSSREFS Cf. A190187. Sequence in context: A295525 A302274 A047112 * A032250 A215790 A133485 Adjacent sequences: A190183 A190184 A190185 * A190187 A190188 A190189 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.)