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Absolute value of the determinant of the matrix whose terms are fibonacci(m+r+s)^(n) with 0 <= r, s <=n, for any m.
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%I #26 Dec 23 2015 11:13:50

%S 1,2,36,13824,324000000,1209323520000000,1923567501916569600000000,

%T 3436011282355888738787131392000000000,

%U 18204541483393435808637499286914987185930240000000000,753091424970084722185225494963366011108371967508480000000000000000000000

%N Absolute value of the determinant of the matrix whose terms are fibonacci(m+r+s)^(n) with 0 <= r, s <=n, for any m.

%H L. Carlitz, <a href="http://www.fq.math.ca/Scanned/4-2/carlitz.pdf">Some Determinants Containing Powers of Fibonacci Numbers</a>, The Fibonacci Quarterly, 4.2 (1966), 129-134.

%H Aram Tangboonduangjit, Thotsaporn Thanatipanonda, <a href="http://arxiv.org/abs/1512.07025">Determinants Containing Powers of Generalized Fibonacci Numbers</a>, arXiv:1512.07025 [math.CO], 2015.

%F a(n) = Product_{j=0..n} binomial(n,j) * Product{j=1..n} fibonacci(j)^(n-j+1))^2.

%F a(n) = A001142(n)*A152686(n)^2.

%o (PARI) a(n) = prod(j=0, n, binomial(n, j)) * prod(j=1,n, fibonacci(j)^(n-j+1))^2;

%Y Cf. A001142, A152686.

%K nonn

%O 1,2

%A _Michel Marcus_, Dec 23 2015