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A001681
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The partition function G(n,4).
(Formerly M1481 N0584)
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6
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1, 1, 2, 5, 15, 51, 196, 827, 3795, 18755, 99146, 556711, 3305017, 20655285, 135399720, 927973061, 6631556521, 49294051497, 380306658250, 3039453750685, 25120541332271, 214363100120051, 1885987611214092, 17085579637664715
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of '12-3 and 321-4'-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 19
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
T. Mansour, Restricted permutations by patterns of type 2-1.
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FORMULA
| E.g.f.: exp( x + x^2/2 + x^3/6 + x^4/24 ). - Ralf Stephan, Apr 22 2004
a(n) = n! * sum(k=1..n, 1/k! * sum(j=0..k, binomial(k,j) * sum(i=j..n-k+j, binomial(j,i-j) * binomial(k-j,n-3*k+3*j-i) * 2^(5*k-4*j+i-2*n) * 3^(j-k)))) [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Jan 25 2011]
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PROG
| (PARI)
A001681(n)=n!*sum(k=1, n, 1/k!*sum(j=0, k, binomial(k, j)*sum(i=j, n-k+j, binomial(j, i-j)*binomial(k-j, n-3*k+3*j-i)*2^(5*k-4*j+i-2*n)*3^(j-k))));
vector(33, n, A001681(n-1)) /* show terms */
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CROSSREFS
| Cf. A001680.
Sequence in context: A108307 A193296 A117426 * A192553 A053553 A007312
Adjacent sequences: A001678 A001679 A001680 * A001682 A001683 A001684
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Ralf Stephan, Apr 22 2004
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