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Search: id:A116482
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| A116482 |
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Triangle read by rows: T(n,k) is the number of partitions of n having k even parts (n>=0, 0<=k<=floor(n/2)). |
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+0
3
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| 1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 3, 1, 4, 4, 2, 1, 5, 6, 3, 1, 6, 8, 5, 2, 1, 8, 11, 7, 3, 1, 10, 14, 10, 5, 2, 1, 12, 19, 14, 7, 3, 1, 15, 24, 19, 11, 5, 2, 1, 18, 31, 26, 15, 7, 3, 1, 22, 39, 34, 21, 11, 5, 2, 1, 27, 49, 45, 29, 15, 7, 3, 1, 32, 61, 58, 39, 22, 11, 5, 2, 1, 38, 76, 75, 52, 30
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row n has 1+floor(n/2) terms. Row sums are the partition numbers (A000041). Column 0 yields A000009. Column 1 yields A038348. Sum(k*T(n,k),k=0..floor(n/2))=A066898(n).
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FORMULA
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G.f.= G(t,x)=1/product((1-x^(2j-1))(1-tx^(2j)),j=1..infinity).
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EXAMPLE
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T(7,2)=3 because we have [4,2,1],[3,2,2], and [2,2,1,1,1].
Triangle starts:
1;
1;
1,1;
2,1;
2,2,1;
3,3,1;
4,4,2,1;
5,6,3,1;
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MAPLE
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g:=1/product((1-x^(2*j-1))*(1-t*x^(2*j)), j=1..20): gser:=simplify(series(g, x=0, 22)): P[0]:=1: for n from 1 to 18 do P[n]:=coeff(gser, x^n) od: for n from 0 to 18 do seq(coeff(P[n], t, j), j=0..floor(n/2)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000041, A066898, A103919, A038348.
Sequence in context: A097368 A109699 A029283 this_sequence A029287 A055184 A035388
Adjacent sequences: A116479 A116480 A116481 this_sequence A116483 A116484 A116485
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 17 2006
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