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A265944 Absolute value of the determinant of the matrix whose terms are fibonacci(m+r+s)^(n) with 0 <= r, s <=n, for any m.

%I A265944 #35 Jan 27 2025 01:49:36
%S A265944 1,2,36,13824,324000000,1209323520000000,1923567501916569600000000,
%T A265944 3436011282355888738787131392000000000,
%U A265944 18204541483393435808637499286914987185930240000000000,753091424970084722185225494963366011108371967508480000000000000000000000
%N A265944 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 A265944 L. Carlitz, <a href="https://web.archive.org/web/2024*/https://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 A265944 Eric Rowland and Jesus Sistos Barron, <a href="https://arxiv.org/abs/2501.14643">Complexity of powers of a constant-recursive sequence</a>, arXiv:2501.14643 [math.NT], 2025. See p. 6.
%H A265944 Aram Tangboonduangjit and 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 A265944 a(n) = (Product_{j=0..n} binomial(n,j)) * (Product_{j=1..n} fibonacci(j)^(n-j+1))^2.
%F A265944 a(n) = A001142(n)*A152686(n)^2.
%o A265944 (PARI) a(n) = prod(j=0, n, binomial(n, j)) * prod(j=1,n, fibonacci(j)^(n-j+1))^2;
%Y A265944 Cf. A001142, A152686.
%K A265944 nonn
%O A265944 1,2
%A A265944 _Michel Marcus_, Dec 23 2015