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A089259
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G.f.: Product_{m>=1} 1/(1-x^m)^A000009(m).
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2
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1, 1, 2, 4, 7, 12, 22, 36, 61, 101, 166, 267, 433, 686, 1088, 1709, 2671, 4140, 6403, 9824, 15028, 22864, 34657, 52288, 78646, 117784, 175865, 261657, 388145, 573936, 846377, 1244475, 1825170, 2669776, 3895833, 5671127, 8236945, 11936594, 17261557, 24909756
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of complete set partitions of the integer partitions of n. This is the Euler transform of A000009. If we change the combstruct command from unlabeled to labeled, then we get A000258. - Thomas Wieder, Aug 01 2008
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..1000
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MAPLE
| with(combstruct): A089259:= [H, {H=Set(T, card>=1), T=PowerSet (Sequence (Z, card>=1), card>=1)}, unlabeled]; 1, seq (count (A089259, size=j), j=1..16); # Thomas Wieder, Aug 01 2008
with (numtheory):
b:= proc(n, i)
if n<0 or n>i*(i+1)/2 then 0
elif n=0 then 1
elif i<1 then 0
else b(n, i):= b(n-i, i-1) +b(n, i-1)
fi
end:
a:= proc(n) option remember; `if` (n=0, 1,
add (add (d* b(d, d), d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq (a(n), n=1..100); # Alois P. Heinz, Nov 11, 2011
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CROSSREFS
| Cf. A001970, A050342, A089254, A000009, A068006.
Sequence in context: A054151 A018176 A135460 * A026713 A002573 A064492
Adjacent sequences: A089256 A089257 A089258 * A089260 A089261 A089262
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 23 2003
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