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A158040 Determinant of power series of gamma matrix with determinant 2!. 12
2, 32, 258, 1664, 9710, 53664, 286762, 1497600, 7691238, 38995360, 195696226, 973894272, 4812812446, 23642953376, 115552680090, 562240972800, 2724987988054, 13161369525408, 63371643947474, 304287501281920, 1457424739149582, 6964697175476128 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms, and offset changed to 1 by Colin Barker, Jul 13 2014
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)