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Search: id:A091602
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| A091602 |
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Triangle: T(n,k) = number of partitions of n such that some part is repeated k times and no part is repeated more than k times. |
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+0
9
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| 1, 1, 1, 2, 0, 1, 2, 2, 0, 1, 3, 2, 1, 0, 1, 4, 3, 2, 1, 0, 1, 5, 4, 3, 1, 1, 0, 1, 6, 7, 3, 3, 1, 1, 0, 1, 8, 8, 6, 3, 2, 1, 1, 0, 1, 10, 12, 7, 5, 3, 2, 1, 1, 0, 1, 12, 15, 11, 6, 5, 2, 2, 1, 1, 0, 1, 15, 21, 14, 10, 5, 5, 2, 2, 1, 1, 0, 1, 18, 26, 20, 12, 9, 5, 4, 2, 2, 1, 1, 0, 1, 22, 35, 25, 18, 11
(list; table; graph; listen)
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OFFSET
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1,4
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FORMULA
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G.f.=G=G(t,x)=sum(t^k*(product((1-x^((k+1)j))/(1-x^j), j=1..infinity)-product((1-x^(kj))/(1-x^j), j=1..infinity)), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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1; 1,1; 2,0,1; 2,2,0,1; 3,2,1,0,1; ...
In the partition 5+2+2+2+1+1, 2 is repeated 3 times, no part is repeated more than 3 times.
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MAPLE
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g:=sum(t^k*(product((1-x^((k+1)*j))/(1-x^j), j=1..50)-product((1-x^(k*j))/(1-x^j), j=1..50)), k=1..50): gser:=simplify(series(g, x=0, 20)): for n from 1 to 13 do P[n]:=coeff(gser, x^n) od: for n from 1 to 13 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Row sums: A000041. Inverse: A091603. Square: A091604.
Columns 1-6: A000009, A091605-A091609. Convergent of columns: A002865.
Sequence in context: A113680 A128187 A133121 this_sequence A035465 A096144 A118401
Adjacent sequences: A091599 A091600 A091601 this_sequence A091603 A091604 A091605
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Jan 23 2004
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