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A115080
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Triangle, read by rows, where T(n,k) equals the dot product of the vector of terms in row n that are to the right of T(n,k) with the vector of terms in column k that are above T(n,k): T(n,k) = Sum_{j=0..n-k-1} T(n,j+k+1)*T(j+k,k) for n > k+1 > 0, with T(n,n) = 1 and T(n,n-1) = n (n>=1).
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8
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1, 1, 1, 3, 2, 1, 11, 5, 3, 1, 50, 20, 7, 4, 1, 257, 94, 31, 9, 5, 1, 1467, 507, 150, 44, 11, 6, 1, 9081, 3009, 853, 218, 59, 13, 7, 1, 60272, 19350, 5251, 1307, 298, 76, 15, 8, 1, 424514, 132920, 35109, 8313, 1881, 390, 95, 17, 9, 1, 3151226, 966962, 249332
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OFFSET
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0,4
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COMMENTS
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Triangle A115085 is the dual of this triangle.
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LINKS
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EXAMPLE
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T(n,k) = [T(n,k+1),T(n,k+2),...,T(n,n)]*[T(k,k),T(k+1,k),...,T(n-1,k)]:
11 = [5,3,1]*[1,1,3] = 5*1 + 3*1 + 1*3;
20 = [7,4,1]*[1,2,5] = 7*1 + 4*2 + 1*5;
94 = [31,9,5,1]*[1,2,5,20] = 31*1 + 9*2 + 5*5 + 1*20;
150 = [44,11,6,1]*[1,3,7,31] = 44*1 + 11*3 + 6*7 + 1*31.
Triangle begins:
1;
1, 1;
3, 2, 1;
11, 5, 3, 1;
50, 20, 7, 4, 1;
257, 94, 31, 9, 5, 1;
1467, 507, 150, 44, 11, 6, 1;
9081, 3009, 853, 218, 59, 13, 7, 1;
60272, 19350, 5251, 1307, 298, 76, 15, 8, 1;
424514, 132920, 35109, 8313, 1881, 390, 95, 17, 9, 1;
3151226, 966962, 249332, 57738, 12315, 2587, 494, 116, 19, 10, 1;
24510411, 7396366, 1873214, 422948, 88737, 17377, 3437, 610, 139, 21, 11, 1;
...
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PROG
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(PARI) {T(n, k)=if(n==k, 1, if(n==k+1, n, sum(j=0, n-k-1, T(n, j+k+1)*T(j+k, k))))}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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