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A104713 Triangle T(n,k) = binomial(n,k), read by rows, 3 <= k <=n .

%I A104713 #14 Aug 08 2015 21:32:05
%S A104713 1,4,1,10,5,1,20,15,6,1,35,35,21,7,1,56,70,56,28,8,1,84,126,126,84,36,
%T A104713 9,1,120,210,252,210,120,45,10,1,165,330,462,462,330,165,55,11,1,220,
%U A104713 495,792,924,792,495,220,66,12,1,286,715,1287,1716
%N A104713 Triangle T(n,k) = binomial(n,k), read by rows, 3 <= k <=n .
%F A104713 T(n,k) = A007318(n,k) for n>=3, 3<=k<=n.
%F A104713 From _Peter Bala_, Jul 16 2013: (Start)
%F A104713 The following remarks assume an offset of 0.
%F A104713 Riordan array (1/(1 - x)^4, x/(1 - x)).
%F A104713 O.g.f.: 1/(1 - t)^3*1/(1 - (1 + x)*t) = 1 + (4 + x)*t + (10 + 5*x + x^2)*t^2 + ....
%F A104713 E.g.f.: (1/x*d/dt)^3 (exp(t)*(exp(x*t) - 1 - x*t - (x*t)^2/2!)) = 1 + (4 + x)*t + (10 + 5*x + x^2)*t^2/2! + ....
%F A104713 The infinitesimal generator for this triangle has the sequence [4,5,6,...] on the main subdiagonal and 0's elsewhere. (End)
%e A104713 First few rows of the triangle are:
%e A104713 1;
%e A104713 4, 1;
%e A104713 10, 5, 1;
%e A104713 20, 15, 6, 1;
%e A104713 35, 35, 21, 7, 1;
%e A104713 56, 70, 56, 28, 8, 1;
%e A104713 ...
%p A104713 A104713 := proc(n,k)
%p A104713         binomial(n,k) ;
%p A104713 end proc;
%p A104713 seq(seq( A104713(n,k),k=3..n),n=3..16) ; # _R. J. Mathar_, Oct 29 2011
%Y A104713 Cf. A007318, A104712, A002662 (row sums).
%K A104713 nonn,tabl,easy
%O A104713 3,2
%A A104713 _Gary W. Adamson_, Mar 19 2005