A374668 a(n) is the permanent of the n-th order Hankel matrix M whose generic element is given by M(i,j) = A317614(i+j-1) with i,j = 1, ..., n.

1, 1, 31, 10254, 12238276, 41596930860, 309346186680924, 4522151204857137264, 116038936382978521700928, 4918677318766771695942334272, 323424014903141386787887115413440, 31725978444319999354629697685162941056, 4460612938377274751881312432310360618154240

Offset: 0

Author

Stefano Spezia, Jul 15 2024

Keywords

• nonn

Comments

The Hankel transform of A317614 has the following polynomial as g.f. 1 + x - x^2 - 624*x^3 - 9216*x^4 + 138240*x^5 - 331776*x^6: the matrices are singular for n > 6.

Examples

			a(7) = 4522151204857137264:
  [  1,   4,  15,  32,  65, 108,  175]
  [  4,  15,  32,  65, 108, 175,  256]
  [ 15,  32,  65, 108, 175, 256,  369]
  [ 32,  65, 108, 175, 256, 369,  500]
  [ 65, 108, 175, 256, 369, 500,  671]
  [108, 175, 256, 369, 500, 671,  864]
  [175, 256, 369, 500, 671, 864, 1105]
which is the singular matrix M of minimal order.
		

Links

• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A317614.

Cf. A000583 (trace of M), A006010 (sum of the 1st row or column of M), A035287 (super- or subdiagonal sum of M), A346174, A374708 (k-th super- or subdiagonal sum of M).

Programs

Mathematica

A317614[n_]:=(1/2)*(n^3 + n*Mod[n,2]); a[n_]:=Permanent[Table[A317614[i+j-1], {i, n}, {j, n}]]; Join[{1}, Array[a, 12]]