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A360857
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Triangle read by rows. T(n, k) = binomial(n, ceil(k/2)) * binomial(n + 1, floor(k/2)).
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3
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1, 1, 1, 1, 2, 6, 1, 3, 12, 12, 1, 4, 20, 30, 60, 1, 5, 30, 60, 150, 150, 1, 6, 42, 105, 315, 420, 700, 1, 7, 56, 168, 588, 980, 1960, 1960, 1, 8, 72, 252, 1008, 2016, 4704, 5880, 8820, 1, 9, 90, 360, 1620, 3780, 10080, 15120, 26460, 26460
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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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Table T(n, k) starts:
[0] 1;
[1] 1, 1;
[2] 1, 2, 6;
[3] 1, 3, 12, 12;
[4] 1, 4, 20, 30, 60;
[5] 1, 5, 30, 60, 150, 150;
[6] 1, 6, 42, 105, 315, 420, 700;
[7] 1, 7, 56, 168, 588, 980, 1960, 1960;
[8] 1, 8, 72, 252, 1008, 2016, 4704, 5880, 8820;
[9] 1, 9, 90, 360, 1620, 3780, 10080, 15120, 26460, 26460.
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MAPLE
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A360857 := (n, k) -> binomial(n, ceil(k/2))*binomial(n + 1, floor(k/2)):
seq(seq(A360857(n, k), k=0..n), n=0..9);
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MATHEMATICA
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Table[Binomial[n, Ceiling[k/2]]Binomial[n+1, Floor[k/2]], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 06 2023 *)
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PROG
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(Python)
from math import comb
def A360857_T(n, k): return comb(n+1, m:=k>>1)**2*(n+1-m)*(n-m)//((m+1)*(n+1)) if k&1 else comb(n+1, m:=k>>1)**2*(n+1-m)//(n+1) # Chai Wah Wu, Feb 28 2023
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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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