A278845 a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = (i+j)^2.

1, 4, 145, 19016, 6176676, 4038562000, 4664347807268, 8698721212922496, 24535712762777208384, 99585504924929052560640, 559305193643176161735904320, 4211594966980674975033969246720, 41428564066728305721531962537124096, 520897493876353116313789796095643304960

Offset: 0

Author

Vaclav Kotesovec, Nov 29 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..37

Crossrefs

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

Programs

Maple

with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> (i+j)^2))):
seq(a(n), n=0..16);  # Vaclav Kotesovec, Nov 29 2016, after Alois P. Heinz

Mathematica

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

PARI

{a(n) = matpermanent(matrix(n, n, i, j, (i+j)^2))}
for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Aug 09 2021

Formula

a(n) ~ c * d^n * (n!)^3 / n, where d = 6.14071825... and c = 1.79385445... - Vaclav Kotesovec, Aug 12 2021