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A051055
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`Connected' alternating sign n X n matrices, i.e. not made from smaller blocks.
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1
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0, 1, 0, 1, 2, 59, 1092, 51412, 3420384, 382912420, 68021283668, 19474443244283, 9025228384142396, 6825775070789988992, 8486240219059861120000, 17454179683586670023001218, 59698062960218238908531091872
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| A003827 factors out the singleton components only, but many alternating sign matrices can be decomposed into larger pieces
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FORMULA
| Sum[a[k]z^k/k!^2, {k, 0, Infinity}]=Log[Sum[r[k]z^k/k!^2, {k, 0, Infinity}] where r[k] is the k-th Robbins number A005130[n].
a[n]=r[n]-(1/n)*sum{k=0..n-1}k*C(n, k)^2*r[n-k]*a[k], n>0, a[0]=0, where c(n, k) is binomial coefficient and r[k] is the k-th Robbins number A005130[n] - Vladeta Jovovic.
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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}}
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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}] (* From Jean-François Alcover, Aug 01 2011, after V. Jovovic *)
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CROSSREFS
| Cf. A003827, A005130.
Sequence in context: A100273 A138982 A142666 * A003827 A139190 A050283
Adjacent sequences: A051052 A051053 A051054 * A051056 A051057 A051058
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KEYWORD
| nice,easy,nonn
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AUTHOR
| D. E. Knuth
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 16 2000
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