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A254632
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Triangle read by rows, T(n, k) = 4^n*[x^k]hypergeometric([3/2, -n], [3], -x), n>=0, 0<=k<=n.
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3
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1, 4, 2, 16, 16, 5, 64, 96, 60, 14, 256, 512, 480, 224, 42, 1024, 2560, 3200, 2240, 840, 132, 4096, 12288, 19200, 17920, 10080, 3168, 429, 16384, 57344, 107520, 125440, 94080, 44352, 12012, 1430, 65536, 262144, 573440, 802816, 752640, 473088, 192192, 45760, 4862
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n,k) = 4^(n-k)*C(n,k)*Catalan(k+1).
sum(k=0..n, T(n,k)) = A025230(n+2).
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EXAMPLE
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[ 1]
[ 4, 2]
[ 16, 16, 5]
[ 64, 96, 60, 14]
[ 256, 512, 480, 224, 42]
[1024, 2560, 3200, 2240, 840, 132]
[4096, 12288, 19200, 17920, 10080, 3168, 429]
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MAPLE
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h := n -> simplify(hypergeom([3/2, -n], [3], -x)):
seq(print(seq(4^n*coeff(h(n), x, k), k=0..n)), n=0..9);
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MATHEMATICA
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T[n_, k_] := 4^(n-k) Binomial[n, k] CatalanNumber[k+1];
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PROG
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(Sage)
A254632 = lambda n, k: (4)^(n-k)*binomial(n, k)*catalan_number(k+1)
for n in range(7): [A254632(n, k) for k in (0..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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