The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A177265 Number of permutations of {1,2,...,n} having exactly one string of consecutive fixed points (including singletons). 3
 1, 1, 4, 12, 57, 321, 2176, 17008, 150505, 1485465, 16170036, 192384876, 2483177809, 34554278857, 515620794592, 8212685046336, 139062777326001, 2494364438359953, 47245095998005060, 942259727190907180, 19737566982241851721, 433234326593362631601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Empirically the partial sums of A000240. - Sean A. Irvine, Jul 12 2022 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..450 FORMULA a(n) = (1/2)[1-(-1)^n] + Sum_{j=1..n} d[j], where d[j] = A000166(n) are the derangement numbers. a(1) = 1, a(2) = 1, a(n) = a(n-1) + n*A000166(n-1). - Daniel Suteu, Jan 25 2018 Conjecture: D-finite with recurrence a(n) +(-n+1)*a(n-1) +(-n+1)*a(n-2) +(n-1)*a(n-3) +(n-2)*a(n-4)=0. - R. J. Mathar, Jul 01 2022 EXAMPLE a(4,1) = 12 because we have (the string of consecutive fixed points is between square brackets): [1]342, [1]423, [12]43, [1234], 3[2]41, 4[2]13, 4[23]1, 24[3]1, 41[3]2, 21[34], 231[4], and 312[4]. MAPLE d := proc (n) options operator, arrow: factorial(n)*(sum((-1)^i/factorial(i), i = 0 .. n)) end proc: a := proc (n) options operator, arrow: 1/2-(1/2)*(-1)^n+add(d(j), j = 1 .. n) end proc; seq(a(n), n = 1 .. 22); MATHEMATICA a[0] = 1; a[n_] := a[n] = n*a[n - 1] + (-1)^n; f[n_] := Sum[(n - k) a[n - k - 1], {k, 0, n - 1}]; Array[f, 20] (* Robert G. Wilson v, Apr 01 2011 *) CROSSREFS Cf. A000166. Column A180192(n,1). Cf. A000240. Sequence in context: A065125 A208940 A209068 * A243923 A192331 A068525 Adjacent sequences: A177262 A177263 A177264 * A177266 A177267 A177268 KEYWORD nonn AUTHOR Emeric Deutsch, May 25 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 20 19:00 EDT 2024. Contains 372720 sequences. (Running on oeis4.)