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A323849 Irregular triangle read by rows: T(n,d) (n >= 1, 0 <= d <= 2n-2) = number of n X n integer-valued matrices M such that M_{1,1}=0, M_{n,n}=d, and M_{(i+1),j} = M_{i,j} + (0 or 1), M_{i,(j+1)} = M_{i,j} + (0 or 1).

%I A323849 #22 Feb 11 2019 15:26:01
%S A323849 1,1,4,1,1,18,44,18,1,1,68,615,1236,615,68,1,1,250,7313,46812,84910,
%T A323849 46812,7313,250,1,1,922,85801,1592348,8241540,14024408,8241540,
%U A323849 1592348,85801,922,1,1,3430,1030330,54926890,759337545,3397542544,5530983756,3397542544,759337545,54926890,1030330,3430,1
%N A323849 Irregular triangle read by rows: T(n,d) (n >= 1, 0 <= d <= 2n-2) = number of n X n integer-valued matrices M such that M_{1,1}=0, M_{n,n}=d, and M_{(i+1),j} = M_{i,j} + (0 or 1), M_{i,(j+1)} = M_{i,j} + (0 or 1).
%D A323849 D. E. Knuth, Email to N. J. A. Sloane, Feb 06 2019.
%H A323849 Alois P. Heinz, <a href="/A323849/b323849.txt">Rows n = 1..15, flattened</a>
%F A323849 T(n,1) = binomial(2n,n) - 2 = A115112(n).
%F A323849 The triangle is symmetric: T(n,d) = T(n,2n-2-d).
%e A323849 Triangle begins:
%e A323849   n\d 0   1     2       3       4        5       6       7     8   9 10
%e A323849   1   1
%e A323849   2   1   4     1
%e A323849   3   1  18    44      18       1
%e A323849   4   1  68   615    1236     615       68       1
%e A323849   5   1 250  7313   46812   84910    46812    7313     250     1
%e A323849   6   1 922 85801 1592348 8241540 14024408 8241540 1592348 85801 922  1
%e A323849   ...
%Y A323849 Columns k=0-2 give: A000012, A115112, A252869.
%Y A323849 T(n,n-1) gives A306372.
%Y A323849 Cf. A323848.
%K A323849 nonn,tabf
%O A323849 1,3
%A A323849 _N. J. A. Sloane_, Feb 07 2019
%E A323849 Edited by _Alois P. Heinz_, Feb 11 2019