1,3

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

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

S. K. Das and N. Deo, Rencontres graphs: a family of bipartite graphs, Fib. Quart., Vol. 25, No. 3, August 1987, 250-262.

I. Kaplansky, Symbolic solution of certain problems in permutations, Bull. Amer. Math. Soc., 50 (1944), 906-914.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 65.

T. D. Noe, Table of n, a(n) for n=1..100

E.g.f. = exp(-x)*(1+x^3)/(1-x)(1-x^2). a(n)=sum((-1)^k*n!/k!, k=0..n-1).

a(n) = n*a(n-1)-(-1)^n*n = A000166(n)-(-1)^n = n*A000166(n-1) = A000387(n+1)*2/(n+1) = A000449(n+2)*6/((n+1)*(n+2))

G.f.: exp(-x)/(1-x)*x . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]

a(3)=3 because the permutations of (1,2,3) with one fixed point are (1,3,2), (3,2,1) and (2,1,3)

a:=n->sum(n!*sum((-1)^k/k!, j=0..n), k=0..n): seq(a(n), n=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2007

restart: G(x):=exp(-x)/(1-x)*x: f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=1..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]

Table[Subfactorial[n]*(n + 1), {n, 0, 21}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]

Cf. A008290, A000166, A000387, etc.

A diagonal of A008291.

Sequence in context: A074435 A039647 A071533 this_sequence A132103 A040018 A019016

Adjacent sequences: A000237 A000238 A000239 this_sequence A000241 A000242 A000243

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)