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A143990
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a(n) = n!*A001515(n-1) with a(0) = 1.
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3
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1, 1, 4, 42, 888, 31920, 1750320, 136115280, 14254007040, 1934091250560, 330078373228800, 69199130042380800, 17481751115946163200, 5237838647954514201600, 1836425205487182172262400, 744852154338379227748608000, 346052141662324885396697088000, 182572078442025253754006986752000
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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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E.g.f.: 1 + sqrt(Pi*x/2) * exp(-(1-x)^2/(2*x)) * erfi((1-x)/sqrt(2*x)).
Sum_{n >= 0} a(n)*x^n/(n!)^2 = exp(1 - sqrt(1-2*x)). (End)
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MATHEMATICA
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With[{m=30}, CoefficientList[Series[Exp[1-Sqrt[1-2*x]], {x, 0, m}], x]*(Range[0, m]!)^2] (* G. C. Greubel, Sep 27 2023 *)
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PROG
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(Magma) [n le 2 select 1 else (n-1)*(2*n-5)*Self(n-1) + (n-1)*(n-2)*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 27 2023
(SageMath)
m=30
P.<x> = PowerSeriesRing(QQ, m+2)
def A143990(n): return (factorial(n))^2*P( exp(1-sqrt(1-2*x)) ).list()[n]
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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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