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A005046
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Number of partitions of a 2n-set into even blocks.
(Formerly M3640)
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15
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1, 1, 4, 31, 379, 6556, 150349, 4373461, 156297964, 6698486371, 337789490599, 19738202807236, 1319703681935929, 99896787342523081, 8484301665702298804, 802221679220975886631, 83877585692383961052499
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Louis Comtet, Analyse Combinatoire Tome II, pages 61-62.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 225, 3rd line of table.
CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.
L. B. W. Jolley, Summation of Series. 2nd ed., Dover, NY, 1961, p. 150.
L. Lovasz, Combinatorial Problems and Exercises, North-Holland, 1993, pp. 15.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
S. R. Finch, Moments of sums
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
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FORMULA
| E.g.f.: exp ( cosh x - 1 ) (or exp(cos(x)-1) ).
Recurrence: a(n) = Sum_{k=1..n} binomial(2*n-1, 2*k-1)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2003
a(n)=sum(1/k!*sum(binomial(k,m)/(2^(m-1))*sum(binomial(m,j)*(2*j-m)^(2*n),j,0,m/2)*(-1)^(k-m),m,0,k),k,1,2*n), n>0 [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 05 2010]
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MAPLE
| a:= proc(n) option remember;
`if` (n=0, 1, add (binomial(2*n-1, 2*k-1) *a(n-k), k=1..n))
end:
seq (a(n), n=0..30);
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MATHEMATICA
| NestList[ Factor[ D[#, {x, 2}]] &, Exp[ Cosh[x] - 1], 16] /. x -> 0
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PROG
| (Maxima) a(n):= sum(1/k!*sum(binomial(k, m)/(2^(m-1))*sum(binomial(m, j) *(2*j-m)^(2*n), j, 0, m/2)*(-1)^(k-m), m, 0, k), k, 1, 2*n); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 05 2010]
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CROSSREFS
| See A156289 for the table of partitions of a 2n-set into k even blocks.
For partitions into odd blocks see A003724 and A136630.
Cf. A000110, A003724.
Sequence in context: A138860 A198865 A145087 * A174324 A195195 A141827
Adjacent sequences: A005043 A005044 A005045 * A005047 A005048 A005049
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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