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%I #31 Apr 02 2022 09:26:08
%S 1,1,2,8,46,352,3364,38656,519446,7996928,138826588,2683604992,
%T 57176039628,1331300646912,33636118326984,916559498182656,
%U 26795449170328038,836606220759859200,27784046218331805100
%N a(n) = (1/Pi)*(2^n/n)*(n-1)!*Integral_{t>=0} (sin(t)/t)^n dt.
%H Seiichi Manyama, <a href="/A099765/b099765.txt">Table of n, a(n) for n = 1..406</a>
%H Sergey Fomin and Grigory Mikhalkin, <a href="http://arxiv.org/abs/0906.3828">Labeled floor diagrams for plane curves</a>, arXiv:0906.3828 [math.AG], 2009-2010. [From _N. J. A. Sloane_, Sep 27 2010]
%H W. Trump, <a href="http://www.trump.de/magic-squares/magic-series/formulae.htm">Magic series</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SincFunction.html">Sinc Function</a>
%F a(n) = (1/n) * Sum_{k=0, floor(n/2)} (-1)^k * binomial(n, k) * (n-2*k)^(n-1).
%F a(n) = A261398(n)/n. - _Vladimir Reshetnikov_, Sep 05 2016
%t Table[1/n Sum[(-1)^k Binomial[n,k](n-2k)^(n-1),{k,0,Floor[n/2]}], {n,20}] (* _Harvey P. Dale_, Oct 21 2011 *)
%o (PARI) a(n)=(1/n)*sum(k=0,floor(n/2),(-1)^k*binomial(n,k)*(n-2*k)^(n-1))
%o (Magma) [(1/n)*(&+[(-1)^j*Binomial(n,j)*(n-2*j)^(n-1): j in [0..Floor(n/2)]]): n in [1..25]]; // _G. C. Greubel_, Apr 01 2022
%o (Sage) [(1/n)*sum((-1)^j*binomial(n,j)*(n-2*j)^(n-1) for j in (0..(n//2))) for n in (1..25)] # _G. C. Greubel_, Apr 01 2022
%Y Cf. A049330, A261398.
%K nonn
%O 1,3
%A _Benoit Cloitre_, Nov 11 2004, Dec 11 2007
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