A204244 - OEIS

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A204244

Symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=i! and f(i,j)=0 otherwise.

2

1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 1, 0, 6, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 24, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 120, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 720, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 5040, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..95.

EXAMPLE

Northwest corner:

1 1 1 1

1 2 0 0

1 0 6 0

1 0 0 24

MATHEMATICA

f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := i!;

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}]] (* A204244 *)

Table[Det[m[n]], {n, 1, 15}] (* A204245 *)

Permanent[m_] :=

With[{a = Array[x, Length[m]]},

Coefficient[Times @@ (m.a), Times @@ a]];

Table[Permanent[m[n]], {n, 1, 14}] (* A203228 *)

CROSSREFS

Cf. A204245, A203228.

Sequence in context: A113045 A309365 A204179 * A083093 A334621 A293899

Adjacent sequences: A204241 A204242 A204243 * A204245 A204246 A204247

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 13 2012

STATUS

approved