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A344563
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T(n, k) = binomial(n - 1, k - 1) * binomial(n, k) * 2^k, T(0, 0) = 1. Triangle read by rows, T(n, k) for 0 <= k <= n.
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0
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1, 0, 2, 0, 4, 4, 0, 6, 24, 8, 0, 8, 72, 96, 16, 0, 10, 160, 480, 320, 32, 0, 12, 300, 1600, 2400, 960, 64, 0, 14, 504, 4200, 11200, 10080, 2688, 128, 0, 16, 784, 9408, 39200, 62720, 37632, 7168, 256, 0, 18, 1152, 18816, 112896, 282240, 301056, 129024, 18432, 512
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OFFSET
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0,3
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LINKS
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EXAMPLE
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[0] 1;
[1] 0, 2;
[2] 0, 4, 4;
[3] 0, 6, 24, 8;
[4] 0, 8, 72, 96, 16;
[5] 0, 10, 160, 480, 320, 32;
[6] 0, 12, 300, 1600, 2400, 960, 64;
[7] 0, 14, 504, 4200, 11200, 10080, 2688, 128;
[8] 0, 16, 784, 9408, 39200, 62720, 37632, 7168, 256;
[9] 0, 18, 1152, 18816, 112896, 282240, 301056, 129024, 18432, 512.
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MAPLE
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aRow := n -> seq(binomial(n-1, k-1)*binomial(n, k)*2^k, k=0..n):
seq(print(aRow(n)), n=0..9);
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MATHEMATICA
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T[n_, k_] := Binomial[n-1, k-1] * Binomial[n, k] * 2^k;
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten
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PROG
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(Python)
from math import comb
def T(n, k):
return comb(n-1, k-1)*comb(n, k)*2**k if k > 0 else k**n
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CROSSREFS
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The coefficients of the associated polynomials are in A103371.
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KEYWORD
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AUTHOR
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STATUS
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approved
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