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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

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