A241122 Type I Minkowski-Siegel mass constants (denominators).

2, 8, 48, 384, 3840, 46080, 645120, 10321920, 2786918400, 2229534720, 735746457600, 5885971660800, 765176315904000, 192824431607808000, 385648863215616000, 12340763622899712000, 18881368343036559360000, 15105094674429247488000

Offset

1,1

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Chapter 16.

Links

Table of n, a(n) for n=1..18.

Steven R. Finch, Minkowski-Siegel mass constants, January 9, 2005. [Cached copy, with permission of the author]

Wikipedia, Smith-Minkowski-Siegel mass formula

Mathematica

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}]

Crossrefs

Cf. A000165, A054909, A054911, A241121.

Sequence in context: A375489 A322339 A000165 * A370677 A370936 A109664

Adjacent sequences: A241119 A241120 A241121 * A241123 A241124 A241125

Keyword

nonn,frac,changed

Author

Jean-François Alcover, Apr 16 2014

Status

approved