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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 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

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Last modified September 11 01:27 EDT 2024. Contains 375813 sequences. (Running on oeis4.)