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A167630
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Riordan array (1/(1-x),xm(x)) where m(x) is the g.f. of Motzkin numbers A001006.
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2
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1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 8, 4, 1, 1, 17, 20, 13, 5, 1, 1, 38, 50, 38, 19, 6, 1, 1, 89, 126, 107, 63, 26, 7, 1, 1, 216, 322, 296, 196, 96, 34, 8, 1, 1, 539, 834, 814, 588, 326, 138, 43, 9, 1, 1, 1374, 2187, 2236, 1728, 1052, 507, 190, 53, 10, 1
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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T(n,0)=1, T(0,k)=0 for k>0, T(n,k)=0 if k>n, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-1,k+1).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 8, 8, 4, 1;
1, 17, 20, 13, 5, 1;
1, 38, 50, 38, 19, 6, 1;
...
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MAPLE
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T:= proc(n, k) option remember; `if`(k=0, 1,
`if`(k>n, 0, T(n-1, k-1)+T(n-1, k)+T(n-1, k+1)))
end:
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MATHEMATICA
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T[_, 0] = T[n_, n_] = 1;
T[n_, k_] /; 0<k<n := T[n, k] = T[n-1, k-1] + T[n-1, k] + T[n-1, k+1];
T[_, _] = 0;
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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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