A176043 a(n) = (2*n-1)*(n-1)^(n-1).
1, 1, 3, 20, 189, 2304, 34375, 606528, 12353145, 285212672, 7360989291, 210000000000, 6562168424053, 222902511206400, 8177627877990831, 322248197941182464, 13574710601806640625, 608742554432415203328, 28953409166021786746195, 1455817098785971890290688, 77158366570752229975835181
Offset: 0
Examples
a(5) = determinant(M_5) = 2304 where M_5 is the matrix [5 1 1 1 1] [1 5 1 1 1] [1 1 5 1 1] [1 1 1 5 1] [1 1 1 1 5] The 20 functions from [3] to [3] with one or zero fixed point are: 0fp : 211,212,231,232,311,312,331,332 1fp : 111,112,131,132, 221,222,321,322, 213,233,313,333
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..100, (corrected by _Peter Luschny_, Jan 19 2019)
Crossrefs
Cf. A174964.
Cf. A007778 (functions from [n] to [n] without fixed point).
Cf. A055897 (functions from [n] to [n] with one fixed point).
Cf. A212291 (bijections of [n] with zero or one fixed point).
Cf. A000166 (bijections of [n] without fixed point).
Cf. A000240 (bijections of [n] with one fixed point).
Programs
-
Magma
[ (2*n-1)*(n-1)^(n-1): n in [1..17] ]; // Klaus Brockhaus, Apr 19 2010
-
Magma
[ Determinant( SymmetricMatrix( &cat[ [ j eq k select n else 1: k in [1..j] ]: j in [1..n] ] ) ): n in [1..17] ]; // Klaus Brockhaus, Apr 19 2010
-
Maple
for n from 2 to 30 do:x:=(2*n-1)*(n-1)^(n-1):print(x) :od:
-
Mathematica
Join[{1},Table[(2n-1)(n-1)^(n-1),{n,2,20}]] (* Harvey P. Dale, Jan 16 2014 *) -
PARI
a(n)=n--; (2*n+1)*n^n \\ Charles R Greathouse IV, Jul 31 2016
Formula
a(n) = (2*n-1)*(n-1)^(n-1).
a(n+1) = n! * [x^n] exp(n*x)*(1 + 2*n*x) for n >= 0. - Stefano Spezia, May 07 2023
Extensions
Edited by Klaus Brockhaus, Apr 19 2010
New interpretation and cross-references by Olivier Gérard, Jul 31 2016
Comments