A110195 a(n) = 11^((n^2-n)/2).

1, 1, 11, 1331, 1771561, 25937424601, 4177248169415651, 7400249944258160101211, 144209936106499234037676064081, 30912680532870672635673352936887453361, 72890483685103052142902866787761839379440139451, 1890591424712781041871514584574319778449301246603238034051

Offset: 0

Author

Philippe Deléham, Sep 07 2005

Keywords

• nonn
• easy
• changed

Comments

Sequence given by the Hankel transform (see A001906 for definition) of A082173 = {1, 1, 12, 155, 2124, 30482, 453432, 6936799, ...}; example : det([1, 1, 12, 155; 1, 12, 155, 2124; 12, 155, 2124, 30482; 155, 2124, 30482, 453432]) = 11^6 = 1771561.

Crossrefs

Cf. A001020, A006125, A047656, A053763, A053764, A109345, A109354, A109493, A109966, A110147, A161680.

Programs

Mathematica

Table[11^((n^2-n)/2),{n,0,20}] (* Harvey P. Dale, Feb 02 2012 *)
Join[{1,1},Table[Det[Table[Binomial[11i,j],{i,n},{j,n}]],{n,10}]] (* Harvey P. Dale, Apr 01 2019 *)

Formula

a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(11i, j).

a(n) = A001020(A161680(n)).

Extensions

a(11) from Harvey P. Dale, Feb 02 2012

a(12) from Jason Yuen, Aug 29 2025