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Search: id:A117274
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| A117274 |
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Triangle read by rows: T(n,k) is the number of partitions of n with no even part repeated and having k 1's (n>=0, 0<=k<=n). |
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+0
3
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| 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 3, 2, 1, 1, 1, 0, 1, 3, 3, 2, 1, 1, 1, 0, 1, 4, 3, 3, 2, 1, 1, 1, 0, 1, 6, 4, 3, 3, 2, 1, 1, 1, 0, 1, 7, 6, 4, 3, 3, 2, 1, 1, 1, 0, 1, 9, 7, 6, 4, 3, 3, 2, 1, 1, 1, 0, 1, 12, 9, 7, 6, 4, 3, 3, 2, 1, 1, 1, 0, 1, 14, 12, 9, 7, 6, 4, 3, 3, 2, 1, 1, 1, 0
(list; table; graph; listen)
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OFFSET
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0,16
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COMMENT
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Row sums yield A001935. T(n,0)=A117275(n). T(n,k)=T(n-k,0)=A117275(n-k). Sum(k*T(n,k),k=0..n)=A117276(n).
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FORMULA
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G.f.=G(t,x)=(1+x^2)*product((1+x^(2k))/(1-x^(2k-1)), k=2..infinity)/(1-tx).
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EXAMPLE
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T(8,2)=3 because we have [6,1,1],[4,2,1,1] and [3,3,1,1].
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MAPLE
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g:=(1+x^2)*product((1+x^(2*k))/(1-x^(2*k-1)), k=2..50)/(1-t*x): gser:=simplify(series(g, x=0, 23)): P[0]:=1: for n from 1 to 14 do P[n]:=sort(coeff(gser, x^n)) od: for n from 0 to 14 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001935, A117275, A117276.
Adjacent sequences: A117271 A117272 A117273 this_sequence A117275 A117276 A117277
Sequence in context: A035212 A068029 A158208 this_sequence A140883 A064744 A135997
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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 06 2006
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