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Search: id:A124419
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| A124419 |
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Number of partitions of the set {1,2,...n} having no blocks that contain both odd and even entries. |
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10
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| 1, 1, 1, 2, 4, 10, 25, 75, 225, 780, 2704, 10556, 41209, 178031, 769129, 3630780, 17139600, 87548580, 447195609, 2452523325, 13450200625, 78697155750, 460457244900, 2859220516290, 17754399678409, 116482516809889
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column 0 of A124418.
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FORMULA
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a(n)=Q[n](1,1,0), 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)=4 because we have 13|24, 1|24|3, 13|2|4, and 1|2|3|4.
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MAPLE
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Q[0]:=1: for n from 1 to 30 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 30 do Q[n]:=Q[n] od: seq(subs({t=1, s=1, x=0}, Q[n]), n=0..30);
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CROSSREFS
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Cf. A000110, A124418, A124420, A124421, A124422, A124423.
Sequence in context: A052829 A001998 A005817 this_sequence A006901 A123422 A123413
Adjacent sequences: A124416 A124417 A124418 this_sequence A124420 A124421 A124422
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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), Oct 31 2006
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