A391789 a(n) is the determinant of the n-th order Hankel matrix M(n) whose generic element is given by M(i,j) = phi(i+j) with i,j = 0, ..., n-1 and M(0,0) = 0.

1, 0, -1, 1, -2, -20, -8, 256, 5920, 24320, -385536, 380928, 109130240, 1048645632, -26955161600, 266634035200, 3857663459328, 28245816836096, -284017798938624, -3430335521030144, -27229528475172864, 4759106956244811776, -163495647996360523776, 1854200168756655685632

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Wikipedia, Hankel matrix.

Example

a(4) = -2:
  [0, 1, 1, 2]
  [1, 1, 2, 2]
  [1, 2, 2, 4]
  [2, 2, 4, 2]

Mathematica

a[n_]:=Det[Table[EulerPhi[i+j], {i, 0, n-1}, {j, 0, n-1}]]; Join[{1}, Array[a, 23]]

Crossrefs

Cf. A000010, A368025, A391788, A391790 (permanent).

Sequence in context: A344545 A076495 A308387 * A058403 A083297 A343927

Adjacent sequences: A391786 A391787 A391788 * A391790 A391791 A391792

Keyword

sign

Author

Stefano Spezia, Dec 20 2025

Status

approved