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A001680
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The partition function G(n,3).
(Formerly M1465 N0579)
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10
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1, 1, 2, 5, 14, 46, 166, 652, 2780, 12644, 61136, 312676, 1680592, 9467680, 55704104, 341185496, 2170853456, 14314313872, 97620050080, 687418278544, 4989946902176, 37286121988256, 286432845428192, 2259405263572480, 18280749571449664, 151561941235370176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of '12-3 and 21-3'-avoiding permutations.
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REFERENCES
| F. L. Miksa, L. Moser and M. Wyman, Restricted partitions of finite sets, Canad. Math. Bull., 1 (1958), 87-96.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009)
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 18
T. Mansour, Restricted permutations by patterns of type 2-1.
Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565
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FORMULA
| E.g.f.: exp ( x + x^2 / 2 + x^3 / 6 ).
a(n) = n! * sum(k=1..n, 1/k! * sum(j=0..k, binomial(k,j) * binomial(j,n-3*k+2*j) * 2^(-n+2*k-j) * 3^(j-k))) [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Jan 25 2011]
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MATHEMATICA
| Table[Sum[n!/(m!2^(n+j-2m)3^(m-j))Binomial[m, j]Binomial[j, n+2j-3m], {m, 0, n}, {j, 0, 3m-n}], {n, 0, 15}]
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CROSSREFS
| Cf. A001681.
Sequence in context: A149897 A124527 A149898 * A107268 A006216 A148337
Adjacent sequences: A001677 A001678 A001679 * A001681 A001682 A001683
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com). More terms added May 13 2009.
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