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

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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Partial sums of A000522.

Equals A002104(n) + 1.

Programs

Mathematica

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

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