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A093581 Numerators of odd moments in the distribution of chord lengths for picked at random on the circumference of a unit circle.

%I A093581 #17 Feb 16 2025 08:32:53
%S A093581 4,32,512,4096,131072,1048576,16777216,134217728,8589934592,
%T A093581 68719476736,1099511627776,8796093022208,281474976710656,
%U A093581 2251799813685248,36028797018963968,288230376151711744
%N A093581 Numerators of odd moments in the distribution of chord lengths for picked at random on the circumference of a unit circle.
%C A093581 Presumably this is the same as A102557? - _Andrew S. Plewe_, Apr 18 2007
%C A093581 A102557(n) equals a(n) for n <= 55000. - _G. C. Greubel_, Oct 20 2024
%H A093581 G. C. Greubel, <a href="/A093581/b093581.txt">Table of n, a(n) for n = 1..828</a>
%H A093581 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CircleLinePicking.html">Circle Line Picking</a>
%F A093581 a(n) = 4*A061549(n-1).
%e A093581 1, 4/Pi, 2, 32/(3*Pi), 6, 512/(15*Pi), 20, 4096/(35*Pi), ...
%t A093581 Table[Power[2, 4*n-2 - DigitCount[n-1,2,1]], {n, 30}] (* _G. C. Greubel_, Oct 20 2024 *)
%o A093581 (Magma)
%o A093581 A093581:= func< n | Power(2, 4*n-2-(&+Intseq(2*(n-1), 2))) >;
%o A093581 [A093581(n): n in [1..30]]; // _G. C. Greubel_, Oct 20 2024
%o A093581 (SageMath)
%o A093581 def A093581(n): return pow(2, 4*n-2 - sum((2*n-2).digits(2)))
%o A093581 [A093581(n) for n in range(1,31)] # _G. C. Greubel_, Oct 20 2024
%Y A093581 Cf. A000984, A001803, A061549, A102557.
%Y A093581 Denominators are A001803*Pi.
%K A093581 nonn,frac
%O A093581 1,1
%A A093581 _Eric W. Weisstein_, Apr 01 2004