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A287696
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Triangle read by rows, T(n,k) = (n!)^3 * [x^k] [z^n] hypergeom([], [1, 1], z)^x for n>=0, 0<=k<=n.
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2
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1, 0, 1, 0, -3, 4, 0, 46, -81, 36, 0, -1899, 3916, -2592, 576, 0, 163476, -375375, 305500, -108000, 14400, 0, -25333590, 63002191, -58725000, 26370000, -5832000, 518400, 0, 6412369860, -16976577828, 17470973569, -9168390000, 2636298000, -400075200, 25401600
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OFFSET
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0,5
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COMMENTS
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The polynomials Sum_{k=0..n} T(n,k) x^k generate the columns of A287698.
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LINKS
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FORMULA
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EXAMPLE
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0: [1]
1: [0, 1]
2: [0, -3, 4]
3: [0, 46, -81, 36]
4: [0, -1899, 3916, -2592, 576]
5: [0, 163476, -375375, 305500, -108000, 14400]
6: [0, -25333590, 63002191, -58725000, 26370000, -5832000, 518400]
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MAPLE
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A287696_row := proc(n) local k; hypergeom([], [1, 1], z); series(%^x, z=0, n+1):
n!^3*coeff(%, z, n); seq(coeff(%, x, k), k=0..n) end:
for n from 0 to 8 do A287696_row(n) od;
A287696_poly := proc(n) local k, x; hypergeom([], [1, 1], z); series(%^x, z=0, n+1):
unapply(n!^3*coeff(%, z, n), x); end:
for n from 0 to 7 do A287696_poly(n) od;
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MATHEMATICA
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T[n_, k_] := (n!)^3 SeriesCoefficient[HypergeometricPFQ[{}, {1, 1}, z]^x, {x, 0, k}, {z, 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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