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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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5
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1, 3, 19, 271, 7365, 326011, 21295783, 1924223799, 229714292041, 35007742568755, 6630796801779771, 1527863209528564063, 420814980652048751629, 136526522051229388285611
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| Index entries for related partition-counting sequences
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FORMULA
| a(n)n=a(n-1)(2n^3-n^2+n+1)+a(n-2)(-3n^3+4n^2+2n-3)+a(n-3)(n^3-2n^2-n+2).
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MATHEMATICA
| 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
| (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
| a(n) = Sum[C(n, k)*A105749(k), 0<=k<=n]
Replace "sequence" by "collection" in comment: A105748.
Replace "sets" by "lists" in comment: A082765.
Sequence in context: A054590 A069344 A173799 * A143597 A115705 A136171
Adjacent sequences: A003008 A003009 A003010 * A003012 A003013 A003014
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 18 2002
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