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A116218
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If X_1,...,X_n is a partition of a 2n-set X into 2-blocks (or pairs) then a(n) is equal to the number of permutations f of X such that f(X_i) != X_i for all i=1,...n.
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5
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0, 20, 592, 35088, 3252608, 437765440, 80766186240, 19580003614976, 6038002429456384, 2308538525796209664, 1071858241055770480640, 594103565746026102722560, 387504996819754568329494528, 293818792387460667662661926912, 256273357771747968541309427187712
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{i=0,..,n} (-2)^i*binomial(n,i)*(2*n-2*i)!.
Recurrence: a(n) = 2*(n-1)*(2*n+1)*a(n-1) + 4*(n-1)*(4*n-3)*a(n-2) + 16*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Mar 20 2014
a(n) ~ sqrt(Pi) * 2^(2*n+1) * n^(2*n+1/2) / exp(2*n). - Vaclav Kotesovec, Mar 20 2014
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EXAMPLE
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a(5)=3252608
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MAPLE
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a:=n->sum((-2)^i*binomial(n, i)*(2*n-2*i)!, i=0..n);
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MATHEMATICA
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Table[Sum[(-2)^i*Binomial[n, i]*(2*n-2*i)!, {i, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 20 2014 *)
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PROG
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(PARI) for(n=1, 25, print1(sum(i=0, n, (-2)^i*binomial(n, i)*(2*n-2*i)!), ", ")) \\ G. C. Greubel, Mar 18 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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