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A204243
Determinant of the n-th principal submatrix of A204242.
3
1, 2, 11, 144, 4149, 251622, 31340799, 7913773980, 4024015413705, 4106387069191890, 8395359475529822355, 34357677843892688699400, 281336437060919094044274525, 4608419756389534634440592965950, 150992374805715685629827976712244775
OFFSET
1,2
FORMULA
a(n) = (1 - Sum_{k=2..n} 1/(2^k-1)) * Product_{k=2..n} (2^k-1) = 2*A005329(n) - A203011(n). - Robert Israel, Nov 30 2015
MAPLE
f:= n -> (1 - add(1/(2^i-1), i=2..n))*mul(2^i-1, i=2..n):
seq(f(n), n=1..30); # Robert Israel, Nov 30 2015
MATHEMATICA
f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := 2^i - 1;
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}]] (* A204242 *)
Table[Det[m[n]], {n, 1, 15}] (* A204243 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}] (* A203011 *)
PROG
(PARI) vector(20, n, matdet(matrix(n, n, i, j, if(i==1, 1, if(j==1, 1, if(i==j, 2^i-1)))))) \\ Colin Barker, Nov 27 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 13 2012
STATUS
approved