A054688 Number of nonnegative integer n X n matrices with sum of elements equal to n; polynomial symmetric functions of matrix of order n.

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

Alois P. Heinz, Table of n, a(n) for n = 0..337

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

Cf. A001700, A007716.

Sequence in context: A272499 A305604 A367444 * A229228 A112650 A006295

Adjacent sequences: A054685 A054686 A054687 * A054689 A054690 A054691

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 19 2000

Extensions

a(15) corrected by Ilya Gutkovskiy, Oct 03 2017

Status

approved