This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099765 #32 Feb 16 2025 08:32:55
%S A099765 1,1,2,8,46,352,3364,38656,519446,7996928,138826588,2683604992,
%T A099765 57176039628,1331300646912,33636118326984,916559498182656,
%U A099765 26795449170328038,836606220759859200,27784046218331805100
%N A099765 a(n) = (1/Pi)*(2^n/n)*(n-1)!*Integral_{t>=0} (sin(t)/t)^n dt.
%H A099765 Seiichi Manyama, <a href="/A099765/b099765.txt">Table of n, a(n) for n = 1..406</a>
%H A099765 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 A099765 W. Trump, <a href="http://www.trump.de/magic-squares/magic-series/formulae.htm">Magic series</a>.
%H A099765 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SincFunction.html">Sinc Function</a>
%F A099765 a(n) = (1/n) * Sum_{k=0, floor(n/2)} (-1)^k * binomial(n, k) * (n-2*k)^(n-1).
%F A099765 a(n) = A261398(n)/n. - _Vladimir Reshetnikov_, Sep 05 2016
%t A099765 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 A099765 (PARI) a(n)=(1/n)*sum(k=0,floor(n/2),(-1)^k*binomial(n,k)*(n-2*k)^(n-1))
%o A099765 (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 A099765 (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 A099765 Cf. A049330, A261398.
%K A099765 nonn
%O A099765 1,3
%A A099765 _Benoit Cloitre_, Nov 11 2004, Dec 11 2007