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1, 3, 11, 39, 139, 503, 1847, 6863, 25739, 97239, 369511, 1410863, 5408311, 20801199, 80233199, 310235039, 1202160779, 4667212439, 18150270599, 70690527599, 275693057639, 1076515748879, 4208197927439, 16466861455199, 64495207366199, 252821212875503
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OFFSET
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0,2
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COMMENTS
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Inverse binomial transform of this is A134761: (the sequence interpolated with ones): (1, 1, 3, 1, 11, 1, 39, 1, 139, ...).
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LINKS
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FORMULA
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n*a(n) = 2*(3*n-2)*a(n-1) - (9*n-14)*a(n-2) + 2*(2*n-5)*a(n-3).
n*(3*n-5)*a(n) = (15*n^2-31*n+12)*a(n-1) - 2*(3*n-2)*(2*n-3)*a(n-2). (End)
G.f.: 2/sqrt(1 - 4*x) - 1/(1 - x).
E.g.f.: 2*exp(2*x)*BesselI(0, 2*x) - exp(x). (End)
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 2*n+1,
((12-31*n+15*n^2) *a(n-1)
-2*(3*n-2)*(2*n-3)*a(n-2)) / (n*(3*n-5)))
end:
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MATHEMATICA
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PROG
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(Magma) [2*(n+1)*Catalan(n)-1: n in [0..40]]; // G. C. Greubel, Apr 06 2024
(SageMath) [2*binomial(2*n, n)-1 for n in range(41)] # G. C. Greubel, Apr 06 2024
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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