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Search: id:A124425
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| A124425 |
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Number of partitions of the set {1,2,...n} having no blocks with all entries of the same parity. |
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+0
2
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| 1, 0, 1, 1, 3, 7, 25, 79, 339, 1351, 6721, 31831, 179643, 979567, 6166105, 37852039, 262308819, 1784037031, 13471274401, 100285059751, 818288740923, 6604485845167, 57836113793305, 502235849694679, 4693153430067699
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Column 0 of A124424.
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FORMULA
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a(n)=Q[n](0,0,1), where the polynomials Q[n]=Q[n](t,s,x) are defined by Q[0]=1; Q[n]=t*dQ[n-1]/dt + x*dQ[n-1]/ds + x*dQ[n-1]/dx + t*Q[n-1] if n is odd and Q[n]=x*dQ[n-1]/dt + s*dQ[n-1]/ds + x*dQ[n-1]/dx + s*Q[n-1] if n is even.
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EXAMPLE
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a(4)=3 because we have 1234, 14|23, and 12|34.
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MAPLE
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Q[0]:=1: for n from 1 to 27 do if n mod 2 = 1 then Q[n]:=expand(t*diff(Q[n-1], t)+x*diff(Q[n-1], s)+x*diff(Q[n-1], x)+t*Q[n-1]) else Q[n]:=expand(x*diff(Q[n-1], t)+s*diff(Q[n-1], s)+x*diff(Q[n-1], x)+s*Q[n-1]) fi od: seq(subs({t=0, s=0, x=1}, Q[n]), n=0..27);
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CROSSREFS
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Cf. A000110, A124418, A124419, A124420, A124421, A124422, A124423, A124424.
Sequence in context: A058781 A100462 A130463 this_sequence A118398 A047974 A129084
Adjacent sequences: A124422 A124423 A124424 this_sequence A124426 A124427 A124428
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 01 2006
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