A165343 First series of Hankel determinants based on A001044(n)=(n!)^2 : a(n)=det(A001044(i+j-2))=det(((i+j-2)!)^2), i,j=1,2...n. Hankel transform of A001044.

1, 3, 656, 58910976, 7213311014731776, 3024546589156405495726080000, 9172616430046109813423337553212211200000000, 377602857972999899635616981177669268254387393789952000000000000

Offset

0,2

Comments

It would be highly desirable to obtain a closed form for a(n).

Links

Table of n, a(n) for n=0..7.

Mathematica

nmax = 15; Table[Det[Table[((i+j-2)!)^2, {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Feb 24 2019 *)

Prog

(PARI) a(n)= matdet(matrix(n+1, , i, j, (i+j-2)!^2)); \\ Ruud H.G. van Tol, Jan 13 2026

Crossrefs

Cf. A055209, A165344 (second series).

Sequence in context: A158600 A092301 A229668 * A278316 A361072 A266639

Adjacent sequences: A165340 A165341 A165342 * A165344 A165345 A165346

Keyword

nonn

Author

Karol A. Penson, Sep 15 2009

Extensions

a(7) added by Ruud H.G. van Tol, Jan 13 2026

Status

approved