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URL: https://oeis.org/A143990

⇱ A143990 - OEIS

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A143990
a(n) = n!*A001515(n-1) with a(0) = 1.
3
1, 1, 4, 42, 888, 31920, 1750320, 136115280, 14254007040, 1934091250560, 330078373228800, 69199130042380800, 17481751115946163200, 5237838647954514201600, 1836425205487182172262400, 744852154338379227748608000, 346052141662324885396697088000, 182572078442025253754006986752000
OFFSET
0,3
LINKS
FORMULA
a(n) = n*(2*n-3)*a(n-1) + n*(n-1)*a(n-2), a(0)=1, a(1)=1. - Sergei N. Gladkovskii, May 17 2013
From G. C. Greubel, Sep 27 2023: (Start)
a(n) = n * A105749(n-1) + [n=0].
a(n) = n! * A144301(n).
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)
MATHEMATICA
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 *)
PROG
(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]
[A143990(n) for n in range(m+1)] # G. C. Greubel, Sep 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 02 2008
STATUS
approved