A158040 Determinant of power series of gamma matrix with determinant 2!.

2, 32, 258, 1664, 9710, 53664, 286762, 1497600, 7691238, 38995360, 195696226, 973894272, 4812812446, 23642953376, 115552680090, 562240972800, 2724987988054, 13161369525408, 63371643947474, 304287501281920, 1457424739149582, 6964697175476128

Offset

1,1

Comments

a(n) = Determinant(A + A^2 + A^3 + A^4 + A^5 + ... + A^n) where A is the submatrix A(1..3,1..3) of the matrix with factorial determinant A = [[1,1,1,1,1,1,...],[1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!.

References

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.

Links

Table of n, a(n) for n=1..22.

Formula

Empirical g.f.: 2*x*(8*x^6 -50*x^4 +64*x^3 -25*x^2 +1) / ((x -1)^2*(2*x -1)^2*(2*x^2 -5*x +1)^2). - Colin Barker, Jul 13 2014

Example

a(1) = Determinant(A) = 2! = 2.

Maple

seq(Determinant(sum(A2^i, i=1..n)), n=1..30);

Prog

(PARI) vector(100, n, matdet(sum(k=1, n, [1, 1, 1 ; 1, 2, 1 ; 1, 2, 3]^k))) \\ Colin Barker, Jul 13 2014

Crossrefs

Cf. A111490.

Sequence in context: A008512 A179074 A035602 * A202746 A212797 A203017

Adjacent sequences: A158037 A158038 A158039 * A158041 A158042 A158043

Keyword

nonn

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Extensions

More terms, and offset changed to 1 by Colin Barker, Jul 13 2014

Status

approved