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A081132
a(n) = (n+1)^n*binomial(n+2,2).
8
1, 6, 54, 640, 9375, 163296, 3294172, 75497472, 1937102445, 55000000000, 1711870023666, 57954652913664, 2120125746145771, 83340051191685120, 3503151123046875000, 156797324626531188736, 7445162356977030877593
OFFSET
0,2
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
LINKS
FORMULA
a(n) = (n+1)^n*binomial(n+2,2).
EXAMPLE
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.
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}]
PROG
(Magma)[((n+1)^n*Binomial(n+2, 2)): n in [0..20]]; // Vincenzo Librandi, Sep 21 2011
(Sage) [(n+1)^n*binomial(n+2, 2) for n in (0..20)] # G. C. Greubel, May 18 2021
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).
Sequence in context: A305602 A367471 A367475 * A158831 A034001 A084062
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved