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A112541 Sum for k=0 to n of (n-k)!* n^k. 1
1, 2, 8, 48, 400, 4390, 60624, 1013404, 19881728, 447085170, 11319529600, 318298578664, 9834869311488, 331059072378814, 12055438037135360, 472096504892128500, 19781301201305534464, 882991510898240350666 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..17.

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 *)

CROSSREFS

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

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Last modified December 15 17:42 EST 2019. Contains 330000 sequences. (Running on oeis4.)