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A097514
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Number of partitions of an n-set without blocks of size 2.
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5
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1, 1, 1, 2, 6, 17, 53, 205, 871, 3876, 18820, 99585, 558847, 3313117, 20825145, 138046940, 959298572, 6974868139, 52972352923, 419104459913, 3446343893607, 29405917751526, 259930518212766, 2376498296500063, 22441988298860757
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n, 2*k)*(2*k-1)!!*Bell(n-2*k). E.g.f.: exp(exp(x)-1-x^2/2). More generally, e.g.f. for number of partitions of an n-set which contain exactly q blocks of size p is x^(p*q)/(q!*p!^q)*exp(exp(x)-1-x^p/p!).
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MAPLE
| g:=exp(exp(x)-1-x^2/2): gser:=series(g, x=0, 31): 1, seq(n!*coeff(gser, x^n), n=1..29); (Deutsch)
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CROSSREFS
| Cf. A000296.
Sequence in context: A148451 A148452 A148453 * A108630 A161408 A150033
Adjacent sequences: A097511 A097512 A097513 * A097515 A097516 A097517
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 26 2004
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2004
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