A112541 a(n) = Sum_{k=0..n} (n-k)! * n^k.

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

G. C. Greubel, Table of n, a(n) for n = 0..350

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

Adjacent sequences: A112538 A112539 A112540 * A112542 A112543 A112544

Keyword

nonn

Author

Roger Cuculière, Dec 17 2005

Extensions

Corrected and extended by Robert G. Wilson v, Dec 22 2005

Status

approved