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A035028
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First differences of A002002.
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3
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4, 20, 104, 552, 2972, 16172, 88720, 489872, 2719028, 15157188, 84799992, 475894200, 2677788492, 15102309468, 85347160608, 483183316512, 2739851422820, 15558315261812, 88462135512712, 503569008273992, 2869602773253884, 16368396446913420, 93449566652932784
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OFFSET
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0,1
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LINKS
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FORMULA
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D-finite with recurrence: (n+2)*a(n) - (7*n+8)*a(n-1) + (7*n-8)*a(n-2) - (n-2)*a(n-3) = 0. - R. J. Mathar, Jan 28 2020
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MATHEMATICA
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Differences[CoefficientList[Series[((1-x)/Sqrt[1-6x+x^2]-1)/2, {x, 0, 30}], x]] (* Harvey P. Dale, Jun 04 2011 *)
With[{P=LegendreP}, Table[(n*(n+2)*P[n+2, 3] -(6*n^2+10*n+1)*P[n+1, 3] +(n+1)*(5*n+ 3)*P[n, 3])/(2*n*(n+1)), {n, 30}]] (* G. C. Greubel, Oct 19 2022 *)
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PROG
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(Magma) I:=[4, 20, 104]; [n le 3 select I[n] else ( (7*n+1)*Self(n-1) - (7*n-15)*Self(n-2) + (n-3)*Self(n-3) )/(n+1): n in [1..30]]; // G. C. Greubel, Oct 19 2022
(SageMath)
def A001850(n): return gen_legendre_P(n, 0, 3)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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