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Search: id:A117408
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| A117408 |
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Triangle read by rows: T(n,k) is the number of partitions of n into odd parts in which the largest part occurs k times (1<=k<=n). |
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+0
3
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| 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 1, 5, 1, 1, 0, 0, 0, 0, 0, 1, 6, 2, 1, 0, 0, 0, 0, 0, 0, 1, 8, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 10, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 12, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 15, 4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,11
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COMMENT
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Row sums yield A000009. T(n,1)=A117409(n). Sum(k*T(n,k),k=1..n)=A092311(n).
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FORMULA
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G.f.=G(t,x)=sum(tx^(2k-1)/[(1-tx^(2k-1))product(1-x^(2i-1), i=1..k-1)], k=1..infinity).
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EXAMPLE
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T(14,2)=4 because we have [7,7],[5,5,3,1],[5,5,1,1,1,1] and [3,3,1,1,1,1,1,1,1,1].
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MAPLE
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g:=sum(t*x^(2*k-1)/(1-t*x^(2*k-1))/product(1-x^(2*i-1), i=1..k-1), k=1..40): gser:=simplify(series(g, x=0, 35)): for n from 1 to 15 do P[n]:=expand(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, A117409, A092311.
Sequence in context: A120630 A089605 A060016 this_sequence A079100 A123262 A070202
Adjacent sequences: A117405 A117406 A117407 this_sequence A117409 A117410 A117411
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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), Mar 13 2006
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