OFFSET
0,5
COMMENTS
A003827 factors out the singleton components only, but many alternating sign matrices can be decomposed into larger pieces.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..90
FORMULA
Sum_{k>=0} a(k)z^k/k!^2 = log(Sum_{k>=0} r(k)z^k/k!^2) where r(k) is the k-th Robbins number A005130(n).
a(n) = r(n) - (1/n)*Sum_{k=0..n-1} k*binomial(n, k)^2*r(n-k)*a(k), n > 0, a(0)=0, where r(k) is the k-th Robbins number A005130(n). - Vladeta Jovovic, Mar 16 2000
EXAMPLE
a(4)=2 because of the alternating sign matrices {{0,1,0,0},{1,-1,1,0},{0,1,-1,1},{0,0,1,0}} and {{0,0,1,0},{0,1,-1,1},{1,-1,1,0},{0,1,0,0}}.
MATHEMATICA
r[n_] = Product[(3k+1)!/(n+k)!, {k, 0, n-1}] ; a[n_] := a[n] = r[n] - (1/n)*Sum[k*Binomial[n, k]^2*r[n-k]*a[k], {k, 0, n-1}]; a[0] = 0; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Aug 01 2011, after Vladeta Jovovic *)
CROSSREFS
KEYWORD
nice,easy,nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Mar 16 2000
STATUS
approved