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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).
4
1, 1, 4, 1, 1, 18, 44, 18, 1, 1, 68, 615, 1236, 615, 68, 1, 1, 250, 7313, 46812, 84910, 46812, 7313, 250, 1, 1, 922, 85801, 1592348, 8241540, 14024408, 8241540, 1592348, 85801, 922, 1, 1, 3430, 1030330, 54926890, 759337545, 3397542544, 5530983756, 3397542544, 759337545, 54926890, 1030330, 3430, 1
OFFSET
1,3
REFERENCES
D. E. Knuth, Email to N. J. A. Sloane, Feb 06 2019.
LINKS
FORMULA
T(n,1) = binomial(2n,n) - 2 = A115112(n).
The triangle is symmetric: T(n,d) = T(n,2n-2-d).
EXAMPLE
Triangle begins:
n\d 0 1 2 3 4 5 6 7 8 9 10
1 1
2 1 4 1
3 1 18 44 18 1
4 1 68 615 1236 615 68 1
5 1 250 7313 46812 84910 46812 7313 250 1
6 1 922 85801 1592348 8241540 14024408 8241540 1592348 85801 922 1
...
CROSSREFS
Columns k=0-2 give: A000012, A115112, A252869.
T(n,n-1) gives A306372.
Cf. A323848.
Sequence in context: A203092 A139167 A211709 * A254442 A340476 A176422
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Feb 07 2019
EXTENSIONS
Edited by Alois P. Heinz, Feb 11 2019
STATUS
approved