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

1,1

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)!.

References

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

Links

Table of n, a(n) for n=1..18.

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

Example

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

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);

Prog

(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

Crossrefs

Cf. A111490, A158040.

Sequence in context: A248384 A355752 A099595 * A233212 A270558 A245398

Adjacent sequences: A158038 A158039 A158040 * A158042 A158043 A158044

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