OFFSET
1,2
COMMENTS
Number of functions f:[n]->[n+1] such that some x in [n] maps to n+1.
Number of switching generators for a power polyadic n-context ({1..k}, ..., {1..k}, <>) with n=k [Theorems 5 and 6, page 81, in Ignatov]. - Dmitry I. Ignatov, Nov 23 2022
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..385
D. I. Ignatov, On closure operators related to maximal tricliques in tripartite hypergraphs, Discrete Appl. Math., 249 (2018), 74-84.
D. I. Ignatov, Supporting iPython code for enumeration of switching generators of power polyadic n-contexts for n=k<6, GitHub repository.
FORMULA
E.g.f.: W(-x)*(x-1)/((1+W(-x))*x), W(x) principal branch of Lambert's function.
a(n) = Sum_{m=1..n} A055864(n, m).
a(n) = Sum_{i=0..n-1} n^i*C(n, i). - Olivier Gérard, Jun 26 2001
With interpolated zeros, ceiling(n/2)^floor(n/2) - floor(n/2)^floor(n/2). - Paul Barry, Jul 13 2005
a(n) = Sum_{k=1..n} (-1)^(n-k)*k!*Stirling2(n,k)*binomial(n+k-1,n). - Vladimir Kruchinin, Sep 20 2015
MATHEMATICA
Table[(n+1)^n-n^n, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 20 2009 *)
PROG
(PARI) vector(20, n, (n+1)^n - n^n) \\ Michel Marcus, Jan 10 2015
(Magma) [(n+1)^n - n^n: n in [1..40]]; // Vincenzo Librandi, Jan 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 20 2000
EXTENSIONS
More terms from Vincenzo Librandi, Jan 11 2015
STATUS
approved