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A110518
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Riordan array (1, x*c(3x)), c(x) the g.f. of A000108.
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6
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1, 0, 1, 0, 3, 1, 0, 18, 6, 1, 0, 135, 45, 9, 1, 0, 1134, 378, 81, 12, 1, 0, 10206, 3402, 756, 126, 15, 1, 0, 96228, 32076, 7290, 1296, 180, 18, 1, 0, 938223, 312741, 72171, 13365, 2025, 243, 21, 1, 0, 9382230, 3127410, 729729, 138996, 22275, 2970, 315, 24, 1, 0
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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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Number triangle: T(0,k) = 0^k, T(n,k) = (k/n)*C(2n-k-1, n-k)*3^(n-k), n > 0, k > 0.
Triangle T(n,k), 0 <= k <= n, read by rows, given by (0, 3, 3, 3, 3, 3, 3, 3, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 23 2014
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EXAMPLE
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Rows begin
1;
0, 1;
0, 3, 1;
0, 18, 6, 1;
0, 135, 45, 9, 1;
0, 1134, 378, 81, 12, 1;
...
Production matrix begins:
0, 1;
0, 3, 1;
0, 9, 3, 1;
0, 27, 9, 3, 1;
0, 81, 27, 9, 3, 1;
0, 243, 81, 27, 9, 3, 1;
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MATHEMATICA
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T[0, 0] := 1; T[0, k_] := 0; T[n_, k_] := (k/n)*3^(n - k)*Binomial[2*n - k - 1, n - k]; Table[T[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 29 2017 *)
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PROG
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(PARI) concat([1], for(n=1, 10, for(k=0, n, print1((k/n)*3^(n-k)*binomial(2*n-k-1, n-k), ", ")))) \\ G. C. Greubel, Aug 29 2017
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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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