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%I #32 Feb 24 2023 02:33:28
%S 1,6,40,336,3456,42240,599040,9676800,175472640,3530096640,
%T 78033715200,1880240947200,49049763840000,1377317368627200,
%U 41421544567603200,1328346084409344000,45249466617298944000,1631723190138961920000
%N a(n) = 2^n*n!*(2*n+1).
%C Denominators of expansion of Integral_{t=0..x} exp(-(t^2)/2) dt = sqrt(Pi/2)*erf(x/sqrt(2)) in powers x^(2*n+1), n >= 0. Numerators are (-1)^n. - _Wolfdieter Lang_, Jun 29 2007
%C a(n) = A009445(n) / A001147(n). - _Reinhard Zumkeller_, Dec 03 2011
%H Vincenzo Librandi, <a href="/A014481/b014481.txt">Table of n, a(n) for n = 0..100</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NormalDistributionFunction.html">Normal Distribution Function</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F Expansion of (1+2x)/(1-2x)^2.
%F G.f.: G(0)/(2*x) - 1/x, where G(k)= 1 - 2*x+ 1/(1 - 2*x*(k+1)/(2*x*(k+1) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 24 2013
%F From _Amiram Eldar_, Jul 31 2020: (Start)
%F Sum_{n>=0} 1/a(n) = sqrt(Pi/2) * erfi(1/sqrt(2)).
%F Sum_{n>=0} (-1)^n/a(n) = sqrt(Pi/2) * erf(1/sqrt(2)). (End)
%o (Magma) [2^n*Factorial(n)*(2*n+1): n in [0..50]]; // _Vincenzo Librandi_, Apr 25 2011
%o (Haskell)
%o a014481 n = a009445 n `div` a001147 n -- _Reinhard Zumkeller_, Dec 03 2011
%Y From _Johannes W. Meijer_, Nov 12 2009: (Start)
%Y Appears in A167572.
%Y Equals row sums of A167583.
%Y (End)
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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