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A131063 Triangle read by rows: T(n,k) = 5*binomial(n,k) - 4 for 0 <= k <= n.

%I A131063 #19 Sep 08 2022 08:45:30
%S A131063 1,1,1,1,6,1,1,11,11,1,1,16,26,16,1,1,21,46,46,21,1,1,26,71,96,71,26,
%T A131063 1,1,31,101,171,171,101,31,1,1,36,136,276,346,276,136,36,1,1,41,176,
%U A131063 416,626,626,416,176,41,1,1,46,221,596,1046,1256,1046,596,221,46,1
%N A131063 Triangle read by rows: T(n,k) = 5*binomial(n,k) - 4  for 0 <= k <= n.
%C A131063 Row sums = A131064: (1, 2, 8, 24, 60, 136, 292, ...), the binomial transform of (1, 1, 5, 5, 5, ...).
%H A131063 Muniru A Asiru, <a href="/A131063/b131063.txt">Rows n=0..100 of triangle, flattened</a>
%F A131063 G.f.: (1-z-t*z+5*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - _Emeric Deutsch_, Jun 20 2007
%e A131063 First few rows of the triangle:
%e A131063   1;
%e A131063   1,  1;
%e A131063   1,  6,  1;
%e A131063   1, 11, 11,  1;
%e A131063   1, 16, 26, 16,  1;
%e A131063   1, 21, 46, 46, 21,  1;
%e A131063   1, 26, 71, 96, 71, 26,  1;
%e A131063   ...
%p A131063 T := proc (n, k) if k <= n then 5*binomial(n, k)-4 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # _Emeric Deutsch_, Jun 20 2007
%t A131063 Table[5*Binomial[n,k] -4, {n,0,10}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 12 2020 *)
%o A131063 (GAP) Print(Flat(List([0..10],n->List([0..n],k->5*Binomial(n,k)-4)))); # _Muniru A Asiru_, Feb 21 2019
%o A131063 (Magma) [5*Binomial(n, k) -4: k in [0..n], n in [0..10]]; // _G. C. Greubel_, Mar 12 2020
%o A131063 (Sage) [[5*binomial(n, k) -4 for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Mar 12 2020
%Y A131063 Cf. A109128, A123203, A131060, A131061, A131064, A131065, A131066, A131067, A131068.
%K A131063 nonn,tabl
%O A131063 0,5
%A A131063 _Gary W. Adamson_, Jun 13 2007
%E A131063 More terms from _Emeric Deutsch_, Jun 20 2007