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A051055 'Connected' alternating sign n X n matrices, i.e., not made from smaller blocks. 2
0, 1, 0, 1, 2, 59, 1092, 51412, 3420384, 382912420, 68021283668, 19474443244283, 9025228384142396, 6825775070789988992, 8486240219059861120000, 17454179683586670023001218, 59698062960218238908531091872 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
A003827 factors out the singleton components only, but many alternating sign matrices can be decomposed into larger pieces.
LINKS
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
Sequence in context: A142666 A349501 A283489 * A003827 A241324 A369952
KEYWORD
nice,easy,nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Mar 16 2000
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)