A158041 Determinant of power series of gamma matrix with determinant 3!.

6, 372, 8862, 148800, 2096886, 26922756, 332847654, 4138425600, 53260806102, 715168132932, 9918365312598, 139707565435200, 1971543518031366, 27670255890476676, 385457279875640742, 5335884957031756800, 73579514340980051958, 1013129779240735463748

Offset: 1

Author

Giorgio Balzarotti, Paolo P. Lava, Mar 11 2009

Keywords

• nonn

Comments

a(n) = Determinant(A + A^2 + A^3 + A^4 + A^5 + ... + A^n) where A is the submatrix A(1..4,1..4) 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)!.

Examples

			a(1) = Determinant(A) = 3! = 6.
		

References

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

Crossrefs

Cf. A111490, A158040.

Programs

Maple

with(LinearAlgebra):
A:= <<1|1|1|1>, <1|2|1|2>, <1|2|3|1>, <1|2|3|4>>:
seq(Determinant(add(A^i, i=1..n)), n=1..30);

PARI

vector(100, n, matdet(sum(k=1, n, [1,1,1,1 ; 1,2,1,2 ; 1,2,3,1 ; 1,2,3,4]^k))) \\ Colin Barker, Jul 13 2014

Formula

Empirical g.f.: -6*x*(6*x^2 -1)*(46656*x^12 -828144*x^10 +2517696*x^9 -3533544*x^8 +2852496*x^7 -1444952*x^6 +475416*x^5 -98154*x^4 +11656*x^3 -639*x^2 +1) / ((x -1)*(6*x -1)*(6*x^4 -22*x^3 +23*x^2 -10*x +1)*(216*x^4 -360*x^3 +138*x^2 -22*x +1)*(216*x^6 -828*x^5 +1284*x^4 -808*x^3 +214*x^2 -23*x +1)). - Colin Barker, Jul 13 2014

Extensions

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