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A190194 a(n) = Sum_{r=0..n-1} Sum_{s=r+1..n} s! * r^(n-s). 4
0, 1, 4, 20, 116, 776, 5912, 50648, 482552, 5065016, 58099832, 723315128, 9715154552, 140051879096, 2157103991672, 35355232693688, 614453167841912, 11287370521073336, 218535622980161912, 4447889360078673848, 94944254697268017272, 2120984032794061422776, 49489160848954807154552, 1203943675008917425902008, 30486416629523244528307832 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The expression a(n)/n! = A190186/A190187 arises in the analysis of bubble sort [Knuth].
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 3, Section 5.2.2, p. 129.
LINKS
MAPLE
f:=proc(n) local t1, r, s;
t1:=add( add(s!*r^(n-s), s=r+1..n), r=0..n-1);
end;
MATHEMATICA
Join[{0}, Table[Sum[n! + Sum[s!*k^(n - s), {s, k + 1, n - 1}], {k, 0, n - 1}], {n, 1, 50}]] (* G. C. Greubel, Dec 28 2017 *)
PROG
(PARI) for(n=0, 30, print1(if(n==0, 0, sum(k=0, n-1, n! + sum(s=k+1, n-1, s!*k^(n-s)))), ", ")) \\ G. C. Greubel, Dec 28 2017
CROSSREFS
Sequence in context: A129378 A078944 A158900 * A370530 A127088 A258666
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 05 2011
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)