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A003011
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Number of permutations of up to n kinds of objects, where each kind of object can occur at most two times.
(Formerly M3071)
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7
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1, 3, 19, 271, 7365, 326011, 21295783, 1924223799, 229714292041, 35007742568755, 6630796801779771, 1527863209528564063, 420814980652048751629, 136526522051229388285611
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OFFSET
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0,2
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COMMENTS
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E.g.f. A(x)=y satisfies 0=(2x^3+2x^2)y''+(-3x^3+4x-1)y'+(x^3-x^2-2x+3)y. - Michael Somos, Mar 15 2004
Number of ways to use the elements of {1,..,k}, 0<=k<=2n, once each to form a sequence of n (possibly empty) sets, each having at most 2 elements. - Bob Proctor, Apr 18 2005
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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n*a(n) = (2*n^3 - n^2 + n + 1)*a(n-1) + (-3*n^3 + 4*n^2 + 2*n - 3)*a(n-2) + (n^3 - 2*n^2 - n + 2)*a(n-3).
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MATHEMATICA
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Table[nn=2n; a=1+x+x^2/2!; Total[Range[0, nn]!CoefficientList[Series[a^n, {x, 0, nn}], x]], {n, 0, 15}] (* Geoffrey Critzer, Dec 23 2011 *)
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PROG
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(PARI) a(n)=local(A); if(n<0, 0, A=(1+x+x^2/2)^n; sum(k=0, 2*n, k!*polcoeff(A, k)))
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CROSSREFS
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a(n) = Sum[C(n, k)*A105749(k), 0<=k<=n]
Replace "sequence" with "collection" in comment: A105748.
Replace "sets" with "lists" in comment: A082765.
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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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