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A099765 a(n) = (1/Pi)*(2^n/n)*(n-1)!*Integral_{t>=0} (sin(t)/t)^n dt. 2

%I

%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 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))

%Y Cf. A049330.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Nov 11 2004, Dec 11 2007

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Last modified August 22 07:17 EDT 2019. Contains 326172 sequences. (Running on oeis4.)