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A078482
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Number of data structures of a certain wreath product type.
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0
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0, 1, 2, 6, 20, 70, 254, 948, 3618, 14058, 55432, 221262, 892346, 3630680, 14885042, 61432382, 255025212, 1064190214, 4461325382, 18780710508, 79357572866, 336466650450, 1431007889744, 6103431668830, 26099839562738, 111877997049648, 480635694869218
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| M. D. Atkinson and T. Stitt, Restricted permutations and the wreath product, Discrete Math., 259 (2002), 19-36.
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FORMULA
| G.f.: (1-3*x+x^2-(1-6*x+7*x^2-2*x^3+x^4)^(1/2))/(2*x).
a(n)=sum(m=1..n+1, (binomial(m,n-m+1)*(sum(i=0..m-1, binomial(m,i)*binomial(2*m-i-2,m-1)))*(-1)^(n-m+1))/m), n>0, a(0)=0. [From Vladimir Kruchinin, May 21 2011]
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PROG
| (Maxima)
a(n):=if n=0 then 0 else sum((binomial(m, n-m+1)*(sum(binomial(m, i)*binomial(2*m-i-2, m-1), i, 0, m-1))*(-1)^(n-m+1))/m, m, 1, n+1); [From Vladimir Kruchinin, May 21 2011]
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CROSSREFS
| Sequence in context: A151284 A049138 A095929 * A049128 A192540 A185202
Adjacent sequences: A078479 A078480 A078481 * A078483 A078484 A078485
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 04 2003
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