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A124421
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Number of partitions of the set {1,2,...n} having no blocks that contain only odd entries.
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7
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1, 0, 1, 1, 5, 9, 52, 130, 855, 2707, 19921, 75771, 614866, 2717570, 24040451, 120652827, 1152972925, 6460552857, 66200911138, 408845736040, 4465023867757, 30083964854141, 348383154017581, 2539795748336375, 31052765897026352
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Column 0 of A124420.
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FORMULA
| a(n)=Q[n](0,1,1), 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
| a(4)=5 because we have 1234, 134|2, 14|23, 12|34 and 123|4.
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MAPLE
| 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: for n from 0 to 27 do Q[n]:=Q[n] od: seq(subs({t=0, s=1, x=1}, Q[n]), n=0..27);
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CROSSREFS
| Cf. A000110, A124418, A124419, A124420, A124422, A124423.
Sequence in context: A173776 A000324 A123817 * A143554 A200440 A179100
Adjacent sequences: A124418 A124419 A124420 * A124422 A124423 A124424
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 31 2006
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