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A094443 Triangular array T(n,k) = Fibonacci(n+3-k)*C(n,k), k=0..n, n>=0.

%I A094443 #7 Sep 08 2022 08:45:13
%S A094443 2,3,2,5,6,2,8,15,9,2,13,32,30,12,2,21,65,80,50,15,2,34,126,195,160,
%T A094443 75,18,2,55,238,441,455,280,105,21,2,89,440,952,1176,910,448,140,24,2,
%U A094443 144,801,1980,2856,2646,1638,672,180,27,2,233,1440,4005,6600,7140,5292,2730,960,225,30,2
%N A094443 Triangular array T(n,k) = Fibonacci(n+3-k)*C(n,k), k=0..n, n>=0.
%H A094443 G. C. Greubel, <a href="/A094443/b094443.txt">Rows n = 0..100 of triangle, flattened</a>
%F A094443 From _G. C. Greubel_, Oct 30 2019: (Start)
%F A094443 T(n,k) = binomial(n,k)*Fibonacci(n-k+3).
%F A094443 Sum_{k=0..n} T(n,k) = Fibonacci(2*n+3).
%F A094443 Sum_{k=0..n} (-1)^k * T(n,k) = (-1)^n * Fibonacci(n-3). (End)
%e A094443 First few rows:
%e A094443    2;
%e A094443    3,  2;
%e A094443    5,  6,  2;
%e A094443    8, 15,  9,  2;
%e A094443   13, 32, 30, 12,  2;
%e A094443   21, 65, 80, 50, 15, 2;
%p A094443 with(combinat): seq(seq(fibonacci(n-k+3)*binomial(n,k), k=0..n), n=0..12); # _G. C. Greubel_, Oct 30 2019
%t A094443 Table[Fibonacci[n-k+3]*Binomial[n,k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Oct 30 2019 *)
%o A094443 (PARI) T(n,k) = binomial(n,k)*fibonacci(n-k+3);
%o A094443 for(n=0,12, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Oct 30 2019
%o A094443 (Magma) [Binomial(n,k)*Fibonacci(n-k+3): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Oct 30 2019
%o A094443 (Sage) [[binomial(n,k)*fibonacci(n-k+3) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Oct 30 2019
%o A094443 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n,k)*Fibonacci(n-k+3) ))); # _G. C. Greubel_, Oct 30 2019
%Y A094443 Cf. A000045, A094435, A094436, A094437, A094438, A094439, A094440, A094441, A094442, A094444.
%K A094443 nonn,tabl
%O A094443 0,1
%A A094443 _Clark Kimberling_, May 03 2004