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A208891 Pascal's triangle matrix augmented with a right border of 1's.

%I A208891 #15 Jul 19 2024 11:36:24
%S A208891 1,1,1,1,1,1,1,2,1,1,1,3,3,1,1,1,4,6,4,1,1,1,5,10,10,5,1,1,1,6,15,20,
%T A208891 15,6,1,1,1,7,21,35,35,21,7,1,1,1,8,28,56,70,56,28,8,1,1,1,9,36,84,
%U A208891 126,126,84,36,9,1,1,1,10,45,120,210,252,210,120,45
%N A208891 Pascal's triangle matrix augmented with a right border of 1's.
%C A208891 The eigensequence of this triangle starts as 1, 2, 4, 9, 23, 65,... (cf. A007476).
%C A208891 The flattened sequence differs from A135225 only by an additional leading 1.
%F A208891 T(n,n)=1. T(n,k) = A007318(n-1,k) for k<n.
%e A208891 First few rows of the triangle =
%e A208891 1;
%e A208891 1, 1;
%e A208891 1, 1, 1;
%e A208891 1, 2, 1, 1;
%e A208891 1, 3, 3, 1, 1;
%e A208891 1, 4, 6, 4, 1, 1;
%e A208891 1, 5, 10, 10, 5, 1, 1;
%e A208891 1, 6, 15, 20, 15, 6, 1, 1;
%e A208891 1, 7, 21, 35, 35, 21, 7, 1, 1;
%e A208891 1, 8, 28, 56, 70, 56, 28, 8, 1, 1;
%e A208891 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 1;
%e A208891 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 1;
%e A208891 ...
%p A208891 208891 := proc(n,k)
%p A208891     if n <0 or k<0 or k>n then
%p A208891         0;
%p A208891     elif n = k then
%p A208891         1 ;
%p A208891     else
%p A208891         binomial(n-1,k) ;
%p A208891     end if;
%p A208891 end proc:
%p A208891 seq(seq(A208891(n,k),k=0..n),n=0..12) ; # _R. J. Mathar_, Jul 19 2024
%Y A208891 Cf. A007318, A007476
%K A208891 nonn,easy,tabl
%O A208891 0,8
%A A208891 _Gary W. Adamson_, Mar 03 2012