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A204249 Permanent of the n-th principal submatrix of A003057. 15
1, 2, 17, 336, 12052, 685080, 56658660, 6428352000, 958532774976, 181800011433600, 42745508545320000, 12203347213269273600, 4158410247782904833280, 1667267950805177583582720, 776990110000329481864608000, 416483579190482716042690560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..36

FORMULA

From Vaclav Kotesovec, Dec 01 2016: (Start)

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 = 0.332303267076220516... and c = 8.89134588451...

(End)

MAPLE

with(LinearAlgebra):

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

seq(a(n), n=0..16);  # Alois P. Heinz, Nov 14 2016

MATHEMATICA

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 *)

PROG

(PARI) {a(n) = matpermanent(matrix(n, n, i, j, i+j))}

for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Dec 21 2018

CROSSREFS

Cf. A000442, A003057, A085750, A085807, A278845, A278847, A278300, A278925, A278926.

Sequence in context: A304857 A007785 A201785 * A242368 A243509 A128159

Adjacent sequences:  A204246 A204247 A204248 * A204250 A204251 A204252

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 14 2012

EXTENSIONS

a(0)=1 prepended and one more term added by Alois P. Heinz, Nov 14 2016

STATUS

approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)