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A112541
a(n) = Sum_{k=0..n} (n-k)! * n^k.
5
1, 2, 8, 48, 400, 4390, 60624, 1013404, 19881728, 447085170, 11319529600, 318298578664, 9834869311488, 331059072378814, 12055438037135360, 472096504892128500, 19781301201305534464, 882991510898240350666, 41828674437875442696192, 2095750482492627217639360
OFFSET
0,2
COMMENTS
This sequence appears in the calculation of the expectation of the number of runs of an n-faced die, stopping when a face appears for the second time.
LINKS
FORMULA
a(n) = Sum_{k=0..n} k! * n^(n-k). - G. C. Greubel, Jan 12 2022
MAPLE
A112541 := proc(n)
add((n-k)!*n^k, k=0..n) ;
end proc:
seq(A112541(n), n=0..13) ; # R. J. Mathar, Dec 16 2015
MATHEMATICA
f[n_]:= Sum[(n-k)!n^k, {k, 0, n}]; Array[f, 17] (* Robert G. Wilson v, , Dec 22 2005 *)
PROG
(Magma) [(&+[Factorial(k)*n^(n-k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Jan 12 2022
(Sage) [sum(factorial(k)*n^(n-k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Jan 12 2022
CROSSREFS
Cf. A000142.
Sequence in context: A229233 A063075 A177386 * A052667 A327904 A006925
KEYWORD
nonn
AUTHOR
Roger Cuculière, Dec 17 2005
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Dec 22 2005
STATUS
approved