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A340262
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T(n, k) = multinomial(n + k/2; n, k/2) if k is even else 0. Triangle read by rows, for 0 <= k <= n.
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0
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1, 1, 0, 1, 0, 3, 1, 0, 4, 0, 1, 0, 5, 0, 15, 1, 0, 6, 0, 21, 0, 1, 0, 7, 0, 28, 0, 84, 1, 0, 8, 0, 36, 0, 120, 0, 1, 0, 9, 0, 45, 0, 165, 0, 495, 1, 0, 10, 0, 55, 0, 220, 0, 715, 0, 1, 0, 11, 0, 66, 0, 286, 0, 1001, 0, 3003, 1, 0, 12, 0, 78, 0, 364, 0, 1365, 0, 4368, 0
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listen;
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OFFSET
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0,6
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LINKS
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EXAMPLE
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Triangle starts:
[0] 1;
[1] 1, 0;
[2] 1, 0, 3;
[3] 1, 0, 4, 0;
[4] 1, 0, 5, 0, 15;
[5] 1, 0, 6, 0, 21, 0;
[6] 1, 0, 7, 0, 28, 0, 84;
[7] 1, 0, 8, 0, 36, 0, 120, 0;
[8] 1, 0, 9, 0, 45, 0, 165, 0, 495;
[9] 1, 0, 10, 0, 55, 0, 220, 0, 715, 0;
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MAPLE
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T := proc(n, k) `if`(k::even, combinat:-multinomial(n + k/2, n, k/2), 0) end:
seq(seq(T(n, k), k=0..n), n=0..11);
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MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!);
T[n_, k_] := If[EvenQ[k], multinomial[n + k/2, {n, k/2}], 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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