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A014235
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Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 1 0 ].
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6
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1, 2, 12, 128, 2100, 48032, 1444212, 54763088, 2540607060, 140893490432, 9170099291892, 690117597121328, 59318536757456340, 5763381455631211232, 627402010180980401652, 75942075645205885599248, 10153054354133705795859540, 1490544499134409408040599232
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} k! * Stirling2(n+1, k+1)^2.
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EXAMPLE
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For n = 2 the 12 matrices are all the 2 X 2 0-1 matrices except
[1 1] [1 0] [0 1] [1 1]
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MAPLE
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f:= n -> add(k!*combinat:-stirling2(n+1, k+1)^2, k = 0 .. n):
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MATHEMATICA
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Table[Sum[StirlingS2[n+1, k+1]^2k!, {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, Jul 04 2011 *)
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PROG
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(Maxima) makelist(sum(stirling2(n+1, k+1)^2*k!, k, 0, n), n, 0, 24); /* Emanuele Munarini, Jul 04 2011 */
(PARI) a(n) = sum(k=0, n, k! * stirling(n+1, k+1, 2)^2); \\ Michel Marcus, Feb 21 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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