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A072526 Numerator of number J(n) arising in computation of second moment of A*_n lattice. 1

%I

%S 0,1,5,19,389,1045,78077,623245,6626426,3301971,92695530505,285361879,

%T 17061288862565,1065000744223,25118392969537,2119645764556535,

%U 147712619442026368532,1188946883458975,240322519506608309910831,9412105864959423959,3368266474732313495945,29482240157146090479193

%N Numerator of number J(n) arising in computation of second moment of A*_n lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 476.

%e 0, 1/12, 5/18, 19/32, 389/375, 1045/648, 78077/33614, ...

%p J := proc(n) option remember; local i; if n <= 1 then 0 else (n!/(8*(n+1)*n^(n-2))) * add( n^k/k!, k=0..n) -n^2/(4*(n+1)) +(1/(n+1))*add( binomial(n,i)*(i/n)^i*( (n-i)/n)^(n-i-1)*J(i), i=1..n-1); fi; end;

%Y Cf. A079479.

%K nonn,frac

%O 1,3

%A _N. J. A. Sloane_, Aug 02 2003

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Last modified September 25 16:13 EDT 2020. Contains 337344 sequences. (Running on oeis4.)