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A052611
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Expansion of e.g.f. 1/(1-2*x-2*x^2).
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2
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1, 2, 12, 96, 1056, 14400, 236160, 4515840, 98703360, 2426941440, 66305433600, 1992646656000, 65328154214400, 2320237766246400, 88746105588940800, 3636883029491712000, 158978387626426368000, 7383729547341987840000
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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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E.g.f.: 1/(1 - 2*x - 2*x^2).
a(n) = 2*n*a(n+1) + 2*n*(n-1)*a(n), a(0) = 1, a(1) = 2.
a(n) = (n!/6) * Sum_{p = RootOf(2*z^2+2*z-1)} (1+2*p)*p^(-n-1).
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MAPLE
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spec := [S, {S=Sequence(Union(Z, Z, Prod(Z, Union(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[1/(1-2x-2x^2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 14 2015 *)
Table[n!*(-I*Sqrt[2])^(n)*ChebyshevU[n, I/Sqrt[2]], {n, 0, 40}] (* G. C. Greubel, Jan 31 2023 *)
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PROG
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(Magma) [n le 2 select n else 2*(n-1)*Self(n-1) + 2*(n-1)*(n-2)*Self(n-2): n in [1..41]]; // G. C. Greubel, Jan 31 2023
(SageMath)
A002605=BinaryRecurrenceSequence(2, 2, 0, 1)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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