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A241121 Type I Minkowski-Siegel mass constants (numerators). 4
1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 31, 31, 691, 42151, 29713, 505121, 642332179, 692319119, 8003636403977, 248112728523287, 593468652605200909, 50904295073459007001, 1015740532498234470066371, 701876707956280018815862361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

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..24.

S. 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] // Numerator, {n, 1, 30}]

CROSSREFS

Cf. A054909, A054911, A241122.

Sequence in context: A040303 A040304 A124517 * A040305 A189120 A102292

Adjacent sequences:  A241118 A241119 A241120 * A241122 A241123 A241124

KEYWORD

nonn,frac

AUTHOR

Jean-Fran├žois Alcover, Apr 16 2014

STATUS

approved

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)