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%I #27 May 09 2016 02:57:59
%S 1,34,1870,83215,3994320,186135312,8771626578,411591708660,
%T 19344810307020,908637119420910,42689423937884208,2005443612183077232,
%U 94214069697350815795,4426039514623184676790,207929935924379904006970
%N Fibonomial coefficients.
%H Vincenzo Librandi, <a href="/A056566/b056566.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = A010048(n+8, 8) = Fibonomial(n+8, 8).
%F G.f.: 1/p(9, n) with p(9, n)= 1 - 34*x - 714*x^2 + 4641*x^3 + 12376*x^4 - 12376*x^5 - 4641*x^6 + 714*x^7 + 34*x^8 - x^9 = (1-x)*(1 + 3*x + x^2)*(1 - 7*x + x^2)* (1 + 18*x + x^2)*(1 - 47*x + x^2) (n=9 row polynomial of signed Fibonomial triangle A055870; see this entry for Knuth and Riordan references).
%F Recursion: a(n) = 47*a(n-1) - a(n-2) + ((-1)^n)*A001658(n), n >= 2, a(0)=1, a(1)=34.
%p with(combinat): a:=n-> 1/65520*fibonacci(n) *fibonacci(n+1) *fibonacci(n+2) *fibonacci(n+3) *fibonacci(n+4)*fibonacci(n+5)*fibonacci(n+6)*fibonacci(n+7): seq(a(n), n=1..17); # _Zerinvary Lajos_, Oct 07 2007
%t a[n_] := (1/65520) Times @@ Fibonacci[n + Range[8]]; Array[a, 20, 0] (* _Giovanni Resta_, May 08 2016 *)
%o (PARI) b(n, k)=prod(j=1, k, fibonacci(n+j)/fibonacci(j));
%o vector(20, n, b(n-1, 8)) \\ _Joerg Arndt_, May 08 2016
%Y Cf. A010048, A000045, A001654-8, A056565, A001906 (signed), A004187, A049660 (signed), A049668.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jul 10 2000
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