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%I #11 Dec 21 2024 02:01:02
%S 2,8,48,384,3840,46080,645120,10321920,2786918400,2229534720,
%T 735746457600,5885971660800,765176315904000,192824431607808000,
%U 385648863215616000,12340763622899712000,18881368343036559360000,15105094674429247488000
%N Type I Minkowski-Siegel mass constants (denominators).
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Chapter 16.
%H Steven R. Finch, <a href="/A241121/a241121.pdf">Minkowski-Siegel mass constants</a>, January 9, 2005. [Cached copy, with permission of the author]
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Smith%E2%80%93Minkowski%E2%80%93Siegel_mass_formula">Smith-Minkowski-Siegel mass formula</a>
%t a[n_ /; 1 <= n <= 8] = 1/(n!*2^n); a[n_ /; n > 8] := (k = Quotient[n, 2]; r = Mod[n, 8]; Switch[r, 0, (1 - 2^-k)*(1 + 2^(1-k))/(k!*2)*BernoulliB[k]*Product[BernoulliB[j], {j, 2, 2k-2, 2}], 1|7, (2^k+1)/(k!*2^(2k+1))*Product[BernoulliB[j], {j, 2, 2k, 2}], 2|6, 1/((k-1)!*2^(2k+1))*EulerE[k-1]*Product[BernoulliB[j], {j, 2, 2k-2, 2}],3|5, (2^k-1)/(k!*2^(2k+1))*Product[BernoulliB[j], {j, 2, 2k, 2}], 4, (1-2^-k)*(1-2^(1-k))/(k!*2)*BernoulliB[k]* Product[BernoulliB[j], {j, 2, 2k-2, 2}], _, Print["error n = ", n]; 0] // Abs); Table[a[n] // Denominator, {n, 1, 30}]
%Y Cf. A000165, A054909, A054911, A241121.
%K nonn,frac
%O 1,1
%A _Jean-François Alcover_, Apr 16 2014