%I #26 Sep 08 2022 08:45:09

%S 1,6,54,640,9375,163296,3294172,75497472,1937102445,55000000000,

%T 1711870023666,57954652913664,2120125746145771,83340051191685120,

%U 3503151123046875000,156797324626531188736,7445162356977030877593

%N a(n) = (n+1)^n*binomial(n+2,2).

%C A diagonal of A081130.

%C a(n) is the sum of all the fixed points in the set of endofunctions on {1,2,...,n+1}, i.e., the functions f:{1,2,...,n+1} -> {1,2,...,n+1}. - _Geoffrey Critzer_, Sep 17 2011

%H Vincenzo Librandi, <a href="/A081132/b081132.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = (n+1)^n*binomial(n+2,2).

%e a(1) = 6 because there are four functions from {1,2} into {1,2}: (1*,1) (1*,2*) (2,1) (2,2*) and the fixed points (marked *) sum to 6.

%p seq((n+1)^n*binomial(n+2,2), n=0..20); # _G. C. Greubel_, May 18 2021

%t Table[n^n*(n+1)/2,{n,20}]

%o (Magma)[((n+1)^n*Binomial(n+2,2)): n in [0..20]]; // _Vincenzo Librandi_, Sep 21 2011

%o (Sage) [(n+1)^n*binomial(n+2,2) for n in (0..20)] # _G. C. Greubel_, May 18 2021

%Y Sequences of the form (n+m)^n*binomial(n+2,2): A081133 (m=0), this sequence (m=1), A081131 (m=2), A053507 (m=3), A081196 (m=4).

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 08 2003