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A126725
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a(1)=0, a(2)=1; for n>2, a(n) = C(n,2)*(1+a(n-2)).
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2
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0, 1, 3, 12, 40, 195, 861, 5488, 31032, 247005, 1706815, 16302396, 133131648, 1483518127, 13978823145, 178022175360, 1901119947856, 27237392830233, 325091511083547, 5175104637744460, 68269217327545080, 1195449171318970491
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OFFSET
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1,3
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COMMENTS
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a(n) is also the maximum number of ways to place node pairs in an area formed by n 1 X 1 squares. - Theodore M. Mishura, Mar 20 2015
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/2)} 2^k*Pochhammer(-n/2,k)*Pochhammer(1/2-n/2,k). - Theodore M. Mishura, Mar 16 2015
a(n) ~ n! * (exp(sqrt(2)) + (-1)^n * exp(-sqrt(2))) / 2^(n/2+1). - Vaclav Kotesovec, Mar 20 2015
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MAPLE
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seq(simplify(hypergeom([1, 1-n/2, 3/2-n/2], [], 2))*(n-1)*n/2, n=1..22); # Mark van Hoeij, May 12 2013
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MATHEMATICA
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nxt[{n_, a_, b_}]:={n+1, b, Binomial[n+1, 2](a+1)}; Transpose[NestList[nxt, {2, 0, 1}, 30]][[2]] (* Harvey P. Dale, Oct 12 2014 *)
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PROG
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(Magma) I:=[0, 1]; [n le 2 select I[n] else Binomial(n, 2)*(1+Self(n-2)): n in [1..35]]; // Vincenzo Librandi, Mar 17 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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Allan L. Edmonds (edmonds(AT)indiana.edu), Feb 13 2007
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EXTENSIONS
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STATUS
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approved
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