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A096579
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Number of partitions of an n-set with exactly one even block.
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9
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0, 1, 3, 7, 25, 91, 329, 1415, 6297, 29431, 151085, 802099, 4506957, 26836083, 165586321, 1074740079, 7268876881, 50985776815, 372854157589, 2820244541675, 22087612114805, 179014336044171, 1495539626297689, 12894921568568999, 114481871464864825
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OFFSET
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1,3
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LINKS
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FORMULA
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E.g.f.: exp(sinh(x))*(cosh(x)-1). More generally, e.g.f. for the number of partitions of n-set with exactly k even blocks is 1/k!*exp(sinh(x))*(cosh(x)-1)^k.
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MAPLE
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b:= proc(n, t) option remember; `if`(n=0, t, add(
`if`(t=1 and j::even, 0, binomial(n-1, j-1)*
b(n-j, `if`(j::even, 1, t))), j=1..n))
end:
a:= n-> b(n, 0):
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MATHEMATICA
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Drop[ Range[0, 24]! CoefficientList[ Series[ E^Sinh[x]*(Cosh[x] - 1), {x, 0, 24}], x], 1] (* Robert G. Wilson v, Aug 17 2004 *)
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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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EXTENSIONS
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STATUS
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approved
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