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%I #12 Feb 02 2023 16:53:05
%S 1,1,1,1,1,1,1,2,2,1,1,3,6,3,1,1,20,60,60,20,1,1,336,6720,10080,6720,
%T 336,1,1,154440,51891840,518918400,518918400,51891840,154440,1,1,
%U 8204716800,1267136462592000,212878925715456000,1419192838103040000,212878925715456000,1267136462592000,8204716800,1
%N Triangular array T(n,k) read by antidiagonals T(n,k) = F(n)!/(F(k)!*F(n-k)!), where F(m) = A000045(m) = m-th Fibonacci number.
%C Analogous to Pascal's triangle, A007318.
%F T(n,k) = F(n)!/(F(k)!*F(n - k)!), where F(m) = A000045(m) = m-th Fibonacci number.
%e First seven rows:
%e 1
%e 1 1
%e 1 1 1
%e 1 2 2 1
%e 1 3 6 3 1
%e 1 20 60 60 20 1
%e 1 336 6720 10080 6720 336 1
%e ...
%p F:= combinat[fibonacci]:
%p T:= (n, k)-> F(n)!/(F(k)!*F(n-k)!):
%p seq(seq(T(n, k), k=0..n), n=0..8); # _Alois P. Heinz_, Jan 30 2023
%t f[n_] := Fibonacci[n];
%t t = Table[f[n]!/(f[k]!*f[n - k]!), {n, 0, 8}, {k, 0, n}]
%t TableForm[t] (* A360208, array *)
%t Flatten[t] (* A360208, sequence *)
%Y Cf. A000045, A007318, A360207.
%K nonn,tabl
%O 0,8
%A _Clark Kimberling_, Jan 30 2023
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