This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A055869 a(n) = (n+1)^n - n^n. 7
 1, 5, 37, 369, 4651, 70993, 1273609, 26269505, 612579511, 15937424601, 457696700077, 14381984674225, 490839666661891, 18080919199832609, 715027614225987601, 30214447801957316865, 1358671297852359767791, 64780942222614703957417, 3264460344339686410876021 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of functions f:[n]->[n+1] such that some x in [n] maps to n+1. LINKS G. C. Greubel, Table of n, a(n) for n = 1..385 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 Row sums of triangle A055864. Cf. A055864, A055858, A045531. Sequence in context: A050351 A129137 A276232 * A208231 A112937 A258378 Adjacent sequences:  A055866 A055867 A055868 * A055870 A055871 A055872 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 20 2000 EXTENSIONS More terms from Vincenzo Librandi, Jan 11 2015 STATUS approved

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

Last modified February 18 09:42 EST 2019. Contains 320249 sequences. (Running on oeis4.)