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A054688
Number of nonnegative integer n X n matrices with sum of elements equal to n; polynomial symmetric functions of matrix of order n.
9
1, 1, 10, 165, 3876, 118755, 4496388, 202927725, 10639125640, 635627275767, 42634215112710, 3172596834321200, 259398433286078100, 23116565732981832150, 2230164446387219893320, 231574204669402103059965, 25751746463640423324267024, 3053419608195531383028424575
OFFSET
0,3
REFERENCES
E. R. Cavalcanti and M. A. Spohn, On the applicability of mobility metrics for user movement pattern recognition in MANETs, in Proceeding MobiWac '13 Proceedings of the 11th ACM international symposium on Mobility management and wireless access, Pages 123-130, ACM New York, NY, USA 2013, ISBN: 978-1-4503-2355-0 doi:10.1145/2508222.2508228
LINKS
FORMULA
a(n) = C(n^2+n-1, n).
a(n) = [x^n] 1/(1 - x)^(n^2). - Ilya Gutkovskiy, Oct 03 2017
MAPLE
a:= n-> binomial(n*(n+1)-1, n):
seq(a(n), n=0..17); # Alois P. Heinz, Oct 22 2021
MATHEMATICA
Table[Binomial[n^2 + n - 1, n], {n, 0, 17}] (* Michael De Vlieger, Oct 05 2017 *)
PROG
(PARI) a(n) = binomial(n^2+n-1, n); \\ Altug Alkan, Oct 03 2017
CROSSREFS
Sequence in context: A272499 A305604 A367444 * A229228 A112650 A006295
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 19 2000
EXTENSIONS
a(15) corrected by Ilya Gutkovskiy, Oct 03 2017
STATUS
approved