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A052565
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E.g.f. (1+x^3-x^4)/(1-x).
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2
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1, 1, 2, 12, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000
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OFFSET
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0,3
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COMMENTS
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Number of partitions of n-set into "lists", in which every even list appears an odd number of times, cf. A000262. - Alois P. Heinz, May 10 2016
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LINKS
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FORMULA
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E.g.f.: (-1+x^4-x^3)/(-1+x).
Recurrence: {a(1)=1, a(0)=1, (-1-n)*a(n)+a(n+1)=0, a(2)=2, a(4)=24, a(3)=12}.
a(n) = n! for n>3.
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MAPLE
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spec := [S, {S=Union(Sequence(Z), Prod(Z, Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(i::even and j::even, 0, b(n-i*j, i-1)*
multinomial(n, n-i*j, i$j)/j!*i!^j), j=0..n/i)))
end:
a:= n-> b(n$2):
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MATHEMATICA
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a[n_] := If[n <= 3, {1, 1, 2, 12}[[n+1]], n!];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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