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Search: id:A116929
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| A116929 |
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Triangle read by rows: T(n,k) is the number of partitions of n into odd parts such that the sum of the parts, counted without multiplicites, is equal to k (n>=1, k>=1). |
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+0
2
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| 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0, 0, 2, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 0, 0, 3, 1, 1, 0, 1, 1, 2, 1, 0, 0, 3, 0, 2, 0, 2, 1, 1, 2, 1, 0, 1, 3, 0, 2, 0, 1, 2, 1, 1, 3, 1, 0, 0, 4, 0, 2, 0, 2, 2, 2, 1, 1, 3, 1, 0, 0, 4, 0, 2, 1, 2, 3, 1, 2, 1, 2, 3
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OFFSET
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1,25
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COMMENT
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Row sums yield A000009. T(n,n)=A000700(n). Sum(k*T(n,k),k=1..n)=A116930(n).
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FORMULA
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G.f.=-1+product(1+t^(2j-1)*x^(2j-1)/(1-x^(2j-1)), j=1..infinity).
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EXAMPLE
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T(10,4)=3 because we have [3,3,3,1], [3,3,1,1,1,1] and [3,1,1,1,1,1,1,1].
Triangle starts:
1;
1,0;
1,0,1;
1,0,0,1;
1,0,0,1,1;
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MAPLE
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g:=-1+product(1+t^(2*j-1)*x^(2*j-1)/(1-x^(2*j-1)), j=1..40): gser:=simplify(series(g, x=0, 20)): for n from 1 to 15 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 15 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000009, A000700, A116930.
Sequence in context: A095408 A133008 A102550 this_sequence A059984 A046675 A076754
Adjacent sequences: A116926 A116927 A116928 this_sequence A116930 A116931 A116932
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
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