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A360667
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Triangle read by rows: T(n,m)=4^(n-1)*C(n,m)*C(3*n/2-2,n-1)/n, for 0 <= m <= n, with T(0,0)=1.
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0
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1, 1, 1, 2, 4, 2, 10, 30, 30, 10, 64, 256, 384, 256, 64, 462, 2310, 4620, 4620, 2310, 462, 3584, 21504, 53760, 71680, 53760, 21504, 3584, 29172, 204204, 612612, 1021020, 1021020, 612612, 204204, 29172, 245760, 1966080, 6881280, 13762560, 17203200, 13762560, 6881280, 1966080, 245760
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: sin(arcsin(216*x^2*(y+1)^2-1)/3)/6+13/12.
G.f.: 1+x*(sqrt(3)/2)*(sech(arccosh(-sqrt(108)*x*(1+y))/3))*(1+y).
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EXAMPLE
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Triangle T(n, m) starts:
[0] 1;
[1] 1, 1;
[2] 2, 4, 2;
[3] 10, 30, 30, 10;
[4] 64, 256, 384, 256, 64;
[5] 462, 2310, 4620, 4620, 2310, 462;
[6] 3584, 21504, 53760, 71680, 53760, 21504, 3584;
[7] 29172, 204204, 612612, 1021020,1021020, 612612, 204204, 29172;
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MATHEMATICA
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T[0, 0] = 1;
T[n_, m_] := 4^(n-1)*Binomial[n, m]*Binomial[3n/2-2, n-1]/n;
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PROG
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(Maxima)
T(n, m):=if n=0 and m=0 then 1 else if n=0 then 0 else (4^(n-1)*binomial(n, m)*binomial((3*n)/2-2, n-1))/(n);
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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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