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A339350
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Triangle read by rows. T(n,k) = Sum_{j=0..k} binomial(k-j+2, 2)*T(n-1, j), for n>=0, 0<=k<=n, with T(0,0)=1 and T(n,n)=0 for n>0.
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1
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1, 1, 0, 1, 3, 0, 1, 6, 15, 0, 1, 9, 39, 91, 0, 1, 12, 72, 272, 612, 0, 1, 15, 114, 570, 1995, 4389, 0, 1, 18, 165, 1012, 4554, 15180, 32890, 0, 1, 21, 225, 1625, 8775, 36855, 118755, 254475, 0, 1, 24, 294, 2436, 15225, 75516, 302064, 949344, 2017356, 0
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OFFSET
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0,5
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 0;
1, 3, 0;
1, 6, 15, 0;
1, 9, 39, 91, 0;
1, 12, 72, 272, 612, 0;
...
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MATHEMATICA
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A339350[n_, k_] := A339350[n, k] = Which[k == 0, 1, n == k, 0, True, Sum[Binomial[k-j+2, 2]*A339350[n-1, j], {j, 0, k}]];
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PROG
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(PARI) T(n, k) = if ((n==0) && (k==0), 1, if (n<=k, 0, sum(j=0, k, binomial(k-j+2, 2)*T(n-1, j))));
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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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