Search: id:A094941
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%I A094941
%S A094941 1,2,2,8,12,64,120,768,1680,12288,30240,245760,665280,5898240,17297280,
%T A094941 165150720,518918400,5284823040,17643225600,190253629440,670442572800,
%U A094941 7610145177600,28158588057600,334846387814400,1295295050649600
%N A094941 n! times coefficient of pi^[n/2] in volume of n-dimensional unit ball.
%C A094941 E.g.f. A(x) satisfies A'(x) = 2+2*x*A(x), A(0)=1.
%D A094941 L. Badger, Generating the Measures of n-Balls, Amer. Math. Monthly, 107 
               (2000), pp. 256-258.
%F A094941 E.g.f.: exp(-x^2)(1+2*Integral_{t=0..x} exp(-t^2) dt). a(n)=(2n-2)a(n-2), 
               if n>1.
%F A094941 a(n)a(n+1)=n!2^(n+1).
%e A094941 The volume of sphere is 4/3*pi*r^3 so 3!*4/3 = 8 = a(3).
%t A094941 Table[If[OddQ[n], 2^n ((n - 1)/2)!, 2(n - 1)!/((n/2 - 1)!)], {n, 1, 25}] 
               - Robert A. Russell (russell(AT)post.harvard.edu), May 07 2006
%o A094941 (PARI) a(n)=local(A); if(n<0,0, A=exp(x^2+x*O(x^n)); n!*polcoeff(A*(1+2*intformal(1/
               A)),n))
%Y A094941 Cf. A087299.
%Y A094941 Sequence in context: A026537 A089248 A006663 this_sequence A002785 A045686 
               A045677
%Y A094941 Adjacent sequences: A094938 A094939 A094940 this_sequence A094942 A094943 
               A094944
%K A094941 nonn
%O A094941 0,2
%A A094941 Michael Somos, May 24 2004

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