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a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = (i+j)^2.
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%I #24 Aug 12 2021 08:45:45

%S 1,4,145,19016,6176676,4038562000,4664347807268,8698721212922496,

%T 24535712762777208384,99585504924929052560640,

%U 559305193643176161735904320,4211594966980674975033969246720,41428564066728305721531962537124096,520897493876353116313789796095643304960

%N a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = (i+j)^2.

%H Vaclav Kotesovec, <a href="/A278845/b278845.txt">Table of n, a(n) for n = 0..37</a>

%F a(n) ~ c * d^n * (n!)^3 / n, where d = 6.14071825... and c = 1.79385445... - _Vaclav Kotesovec_, Aug 12 2021

%p with(LinearAlgebra):

%p a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> (i+j)^2))):

%p seq(a(n), n=0..16); # _Vaclav Kotesovec_, Nov 29 2016, after _Alois P. Heinz_

%t Flatten[{1, Table[Permanent[Table[(i+j)^2, {i, 1, n}, {j, 1, n}]], {n, 1, 15}]}]

%o (PARI) {a(n) = matpermanent(matrix(n, n, i, j, (i+j)^2))}

%o for(n=0, 20, print1(a(n), ", ")) \\ _Vaclav Kotesovec_, Aug 09 2021

%Y Cf. A005249, A085750, A085807, A204249, A278847.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Nov 29 2016