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A259239
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E.g.f.: exp(x-sqrt(1-x^2)+1).
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3
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1, 1, 2, 4, 13, 41, 211, 967, 7274, 44578, 449551, 3456641, 43883797, 405589549, 6212792678, 67022223556, 1202604514141, 14825243365517, 304950638503279, 4227716923246963, 98067246206824406, 1509933505953992386, 38990856819985996927, 660048542856323263589, 18778057160849966289433
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = ((2*n-3)*a(n-1) + (n-1)*(n^2-5*n+5)*a(n-2) + 2*(n-1)*(n-2)*(n-3)*(a(n-4)-a(n-3)))/(n-2) for n >= 4. - Alois P. Heinz, Jan 30 2020
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MAPLE
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a:= proc(n) option remember; `if`(n<4, [1$2, 2, 4][n+1],
((2*n-3)*a(n-1) +(n-1)*(n^2-5*n+5)*a(n-2)
+2*(n-1)*(n-2)*(n-3)*(a(n-4)-a(n-3)))/(n-2))
end:
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MATHEMATICA
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CoefficientList[Series[E^(x-Sqrt[1-x^2]+1), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jun 22 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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