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A204249
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Permanent of the n-th principal submatrix of A003057.
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18
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1, 2, 17, 336, 12052, 685080, 56658660, 6428352000, 958532774976, 181800011433600, 42745508545320000, 12203347213269273600, 4158410247782904833280, 1667267950805177583582720, 776990110000329481864608000, 416483579190482716042690560000
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OFFSET
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0,2
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COMMENTS
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I have proved that for any odd prime p we have a(p) == p (mod p^2). - Zhi-Wei Sun, Aug 30, 2021
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LINKS
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FORMULA
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a(n) ~ c * d^n * (n!)^2 / sqrt(n), where d = A278300 = 2.455407482284127949... and c = 1.41510164826...
a(n) ~ c * d^n * n^(2*n + 1/2), where d = A278300/exp(2) = 0.332303267076220516... and c = 8.89134588451...
(End)
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MAPLE
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with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> i+j))):
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MATHEMATICA
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f[i_, j_] := i + j;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
{n, 1, 12}, {i, 1, n}]] (* A003057 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}] (* A204249 *)
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PROG
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(PARI) {a(n) = matpermanent(matrix(n, n, i, j, i+j))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(0)=1 prepended and one more term added by Alois P. Heinz, Nov 14 2016
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STATUS
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approved
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