

A003011


Number of permutations of up to n kinds of objects, where each kind of object can occur at most two times.
(Formerly M3071)


7



1, 3, 19, 271, 7365, 326011, 21295783, 1924223799, 229714292041, 35007742568755, 6630796801779771, 1527863209528564063, 420814980652048751629, 136526522051229388285611
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OFFSET

0,2


COMMENTS

E.g.f. A(x)=y satisfies 0=(2x^3+2x^2)y''+(3x^3+4x1)y'+(x^3x^22x+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


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).


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..230
Robert A. Proctor, Let's Expand Rota's Twelvefold Way For Counting Partitions!, arXiv:math.CO/0606404, Jan 05, 2007
Index entries for related partitioncounting sequences


FORMULA

n*a(n) = (2*n^3  n^2 + n + 1)*a(n1) + (3*n^3 + 4*n^2 + 2*n  3)*a(n2) + (n^3  2*n^2  n + 2)*a(n3).
a(n) ~ sqrt(Pi)*2^(n+1)*n^(2*n+1/2)/exp(2*n1).  Vaclav Kotesovec, Oct 19 2013


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 *)


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)))


CROSSREFS

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.
Sequence in context: A316294 A233240 A173799 * A231620 A268646 A143597
Adjacent sequences: A003008 A003009 A003010 * A003012 A003013 A003014


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Vladeta Jovovic, Aug 18 2002


STATUS

approved



