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A291929 Triangle read by rows: T(n,k) = T(n-k,k-1) + 2*T(n-k,k) + T(n-k,k+1) with T(0,0) = 1 for 0 <= k <= A003056(n).

%I A291929 #13 Sep 06 2017 11:05:11
%S A291929 1,0,1,0,2,0,4,1,0,9,2,0,20,6,0,46,13,1,0,105,32,2,0,242,73,6,0,557,
%T A291929 171,15,0,1285,394,36,1,0,2964,914,85,2,0,6842,2109,201,6,0,15793,
%U A291929 4877,467,15,0,36463,11261,1086,38,0,84187,26014,2517,89,1,0,194388
%N A291929 Triangle read by rows: T(n,k) = T(n-k,k-1) + 2*T(n-k,k) + T(n-k,k+1) with T(0,0) = 1 for 0 <= k <= A003056(n).
%H A291929 Seiichi Manyama, <a href="/A291929/b291929.txt">Rows n = 0..481, flattened</a>
%e A291929 First few rows are:
%e A291929   1;
%e A291929   0,    1;
%e A291929   0,    2;
%e A291929   0,    4,   1;
%e A291929   0,    9,   2;
%e A291929   0,   20,   6;
%e A291929   0,   46,  13,  1;
%e A291929   0,  105,  32,  2;
%e A291929   0,  242,  73,  6;
%e A291929   0,  557, 171, 15;
%e A291929   0, 1285, 394, 36, 1.
%Y A291929 Row sums give A291930.
%Y A291929 Columns 0-1 give A000007, A006958 (for n>0).
%Y A291929 Cf. A008289, A291895.
%K A291929 nonn,tabf
%O A291929 0,5
%A A291929 _Seiichi Manyama_, Sep 06 2017