A001338 -1 + Sum (k-1)! C(n,k), k = 1..n for n > 0, a(0) = 1. (Formerly M1759 N0697)

1, 0, 2, 7, 23, 88, 414, 2371, 16071, 125672, 1112082, 10976183, 119481295, 1421542640, 18348340126, 255323504931, 3809950977007, 60683990530224, 1027542662934914, 18430998766219335, 349096664728623335, 6962409983976703336, 145841989688186383358

Offset

0,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..100

E. Biondi, L. Divieti, G. Guardabassi, Counting paths, circuits, chains and cycles in graphs: A unified approach, Canad. J. Math. 22 1970 22-35.

Formula

Conjecture: a(n) +(-n-1)*a(n-1) +2*(n-1)*a(n-2) +(-n+2)*a(n-3)=0. - R. J. Mathar, Feb 16 2014

a(n) = n*a(n-1) - (n-1)*a(n-2) - 1, with a sign reversal for n>=2. - Richard R. Forberg, Dec 16 2014

Mathematica

Join[{1}, Table[-1 + Sum[(k - 1)! Binomial[n, k], {k, n}], {n, 20}]] (* T. D. Noe, Jun 28 2012 *)

Crossrefs

Partial sums of A000522.

Equals A002104(n) + 1.

Sequence in context: A150339 A150340 A339038 * A150341 A150342 A124190

Adjacent sequences: A001335 A001336 A001337 * A001339 A001340 A001341

Keyword

nonn

Author

N. J. A. Sloane

Status

approved