0,2

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 151.

J. Leech, Some sphere packings in higher space, Canad. J. Math., 16 (1964), 657-682.

C. Muses, The dimensional family approach in (hyper)sphere packing..., Applied Math. Computation 88 (1997), pp. 1-26, see p. 22.

Robert L. Griess Jr. Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices. Mar 28 2004. See Proposition 8.9.

G. Nebe and N. J. A. Sloane, Table of highest kissing numbers known

Index entries for sequences related to Barnes-Wall lattices

(2+2)(2+4)(2+8)(2+16)...(2+2^n ).

Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Sep 16 2009: (Start)

G.f.: Sum_{n>=0} 2^(n*(n+1)/2) * x^n/[Product_{k=1..n+1} (1-2^k*x)];

contrast with:

1 = Sum_{n>=0} 2^(n*(n+1)/2) * x^n/[Product_{k=1..n+1} (1+2^k*x)]. (End)

a[0]:=1: for n from 1 to 16 do a[n]:=(2^n+2)*a[n-1] od: seq(a[n], n=0..16); (Deutsch)

(PARI) {a(n)=polcoeff(sum(m=0, n, 2^(m*(m+1)/2)*x^m/prod(k=1, m+1, 1-2^k*x+x*O(x^n))), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 16 2009]

Cf. A028362. [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 16 2009]

Sequence in context: A052718 A061640 A126391 this_sequence A141013 A095340 A141014

Adjacent sequences: A006085 A006086 A006087 this_sequence A006089 A006090 A006091

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), John Leech

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 10 2004

Replaced arXiv URL by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009