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A299845
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a(n) = hypergeom([-n, n - 1], [1], -4).
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3
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1, 1, 25, 425, 7025, 116625, 1951625, 32903225, 558265825, 9522632225, 163160773625, 2806202183625, 48420275891025, 837813745045425, 14531896733426025, 252593595973313625, 4398859688478578625, 76733590756134492225, 1340547988367851940825, 23451231922182584693225
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OFFSET
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0,3
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..798
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FORMULA
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4*n*(n-2)^2*a(n)+4*(n-1)^2*(n-3)*a(n-2)-4*(2*n-3)*(9*n^2-27*n+17)*a(n-1)=0. - Robert Israel, Mar 21 2018
a(n) ~ 2^(-3/2) * 5^(3/4) * phi^(6*n - 3) / sqrt(Pi*n), where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jul 05 2018
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MAPLE
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f:= gfun:-rectoproc({4*n*(n-2)^2*a(n)+4*(n-1)^2*(n-3)*a(n-2)-4*(2*n-3)*(9*n^2-27*n+17)*a(n-1)=0,
a(0)=1, a(1)=1, a(2)=25}, a(n), remember):
map(f, [$0..100]); # Robert Israel, Mar 21 2018
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MATHEMATICA
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a[n_] := Hypergeometric2F1[-n, n - 1, 1, -4]; Table[a[n], {n, 0, 19}]
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CROSSREFS
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Cf. A299506, A243946, A084769, A243947.
Cf. A300945, A300946.
Sequence in context: A020593 A025951 A021944 * A020499 A226712 A020577
Adjacent sequences: A299842 A299843 A299844 * A299846 A299847 A299848
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KEYWORD
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nonn
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AUTHOR
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Peter Luschny, Mar 16 2018
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STATUS
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approved
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