A081132 a(n) = (n+1)^n*binomial(n+2,2).

1, 6, 54, 640, 9375, 163296, 3294172, 75497472, 1937102445, 55000000000, 1711870023666, 57954652913664, 2120125746145771, 83340051191685120, 3503151123046875000, 156797324626531188736, 7445162356977030877593

Offset: 0

Author

Paul Barry, Mar 08 2003

Keywords

• easy
• nonn

Comments

A diagonal of A081130.

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

Examples

			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.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

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).

Programs

Magma

[((n+1)^n*Binomial(n+2,2)): n in [0..20]]; // Vincenzo Librandi, Sep 21 2011

Maple

seq((n+1)^n*binomial(n+2,2), n=0..20); # G. C. Greubel, May 18 2021

Mathematica

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

Sage

[(n+1)^n*binomial(n+2,2) for n in (0..20)] # G. C. Greubel, May 18 2021

Formula

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