A051055 'Connected' alternating sign n X n matrices, i.e., not made from smaller blocks.

0, 1, 0, 1, 2, 59, 1092, 51412, 3420384, 382912420, 68021283668, 19474443244283, 9025228384142396, 6825775070789988992, 8486240219059861120000, 17454179683586670023001218, 59698062960218238908531091872

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

Cf. A003827, A005130.

Sequence in context: A142666 A349501 A283489 * A003827 A241324 A369952

Adjacent sequences: A051052 A051053 A051054 * A051056 A051057 A051058

Keyword

nice,easy,nonn

Author

Don Knuth

Extensions

More terms from Vladeta Jovovic, Mar 16 2000

Status

approved