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Triangle generated by Pascal's rule with left diagonal = [1,0,2,0,3,0,4,...] (A000027 with interpolated zeros) and right diagonal = [1,1,1,1,1,...].
2

%I #12 Sep 19 2024 04:17:08

%S 1,0,1,2,1,1,0,3,2,1,3,3,5,3,1,0,6,8,8,4,1,4,6,14,16,12,5,1,0,10,20,

%T 30,28,17,6,1,5,10,30,50,58,45,23,7,1,0,15,40,80,108,103,68,30,8,1,6,

%U 15,55,120,188,211,171,98,38,9,1,0,21,70,175,308,399,382,269,136,47,10,1

%N Triangle generated by Pascal's rule with left diagonal = [1,0,2,0,3,0,4,...] (A000027 with interpolated zeros) and right diagonal = [1,1,1,1,1,...].

%F T(2*n,n) = A116914(n).

%F Sum_{k=0..n} T(n,k) = A034299(n).

%e Triangle begins:

%e 1;

%e 0, 1;

%e 2, 1, 1;

%e 0, 3, 2, 1;

%e 3, 3, 5, 3, 1;

%e 0, 6, 8, 8, 4, 1;

%e 4, 6, 14, 16, 12, 5, 1;

%e 0, 10, 20, 30, 28, 17, 6, 1;

%Y Cf. A034299, A116914.

%K nonn,tabl,easy

%O 0,4

%A _Philippe Deléham_, Mar 08 2007

%E More terms from _Jason Yuen_, Sep 19 2024