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%I #8 Dec 22 2017 05:15:50
%S 1,2,3,5,9,10,14,28,34,35,42,90,117,125,126,132,297,407,451,461,462,
%T 429,1001,1430,1638,1703,1715,1716,1430,3432,5070,5980,6330,6420,6434,
%U 6435,4862,11934,18122,21930,23630,24174,24293
%N T(n, k) = S(2*n + 1, n, k + 1) for 0<=k<=n and n >= 0, array S as in A050157.
%F T(n, k) = Sum_{0<=j<=k} t(n, j), array t as in A039598.
%F T(n, k) = binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1). _Peter Luschny_, Dec 22 2017
%e Triangle starts:
%e 1
%e 2, 3
%e 5, 9, 10
%e 14, 28, 34, 35
%e 42, 90, 117, 125, 126
%e 132, 297, 407, 451, 461, 462
%e 429, 1001, 1430, 1638, 1703, 1715, 1716
%p A050158 := (n, k) -> binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1):
%p seq(seq(A050158(n,k), k=0..n), n=0..6); # _Peter Luschny_, Dec 22 2017
%Y T(n, 0) = A000108(n+1).
%Y T(n, 1) = A000245(n+1).
%Y T(n, n) = A001700(n).
%Y T(n,n-1) = A010763(n).
%Y Row sums are A296770.
%Y Cf. A039598, A050157.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_
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