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A297628 Seidel's triangle generating A006846 read by rows, T(n,k) for n>=0 and 0<=k<=n.

%I A297628 #7 Jan 02 2018 11:24:07
%S A297628 1,1,1,1,2,2,1,5,7,7,1,20,34,41,41,1,137,253,335,376,376,1,1478,2818,
%T A297628 3905,4657,5033,5033,1,22925,44371,62999,77722,87788,92821,92821,1,
%U A297628 481448,939970,1354121,1705273,1978703,2164345,2257166,2257166
%N A297628 Seidel's triangle generating A006846 read by rows, T(n,k) for n>=0 and 0<=k<=n.
%e A297628 Triangle starts:
%e A297628 0: [1]
%e A297628 1: [1,       1]
%e A297628 2: [1,       2,       2]
%e A297628 3: [1,       5,       7,        7]
%e A297628 4: [1,      20,      34,       41,       41]
%e A297628 5: [1,     137,     253,      335,      376,      376]
%e A297628 6: [1,    1478,    2818,     3905,     4657,     5033,     5033]
%e A297628 7: [1,   22925,   44371,    62999,    77722,    87788,    92821,    92821]
%e A297628 8: [1,  481448,  939970,  1354121,  1705273,  1978703,  2164345,  2257166,  2257166]
%o A297628 (Julia)
%o A297628 function  A297628Triangle(len::Int)
%o A297628     A = fill(BigInt(0), len+1); A[1] = 1
%o A297628     for n in 1:len
%o A297628         for k in n:-1:2 A[k] += A[k+1] end
%o A297628         for k in 2: 1:n A[k] += A[k-1] end
%o A297628         println(A[1:n])
%o A297628     end
%o A297628 end
%o A297628 println(A297628Triangle(9))
%Y A297628 T(n,1) = A297629(n).
%Y A297628 T(n,n) = A006846(n).
%Y A297628 Row sums are A297630.
%K A297628 nonn,tabl
%O A297628 0,5
%A A297628 _Peter Luschny_, Jan 02 2018