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A116860
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Triangle read by rows: T(n,k) is the number of partitions into distinct odd parts with smallest part k (n>=1, k>=1).
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2
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1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,50
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COMMENTS
| Row 2 has no terms, row 2n-1 has 2n-1 terms, row 4n has 2n-1 terms, row 4n+2 for n>=1 has 2n-1 terms. Row sums are A000700. T(n,1)=A027349(n). Sum(k*T(n,k), k>=1)=A092319(n).
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FORMULA
| G.f.=sum(t^(2j-1)*x^(2j-1)*product(1+x^(2i-1), i=j+1..infinity), j=1..infinity).
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EXAMPLE
| T(25,3)=3 because we have [17,5,3], [15,7,3] and [13,9,3].
Triangle starts:
1;
{}
0,0,1;
1;
0,0,0,0,1;
1;
0,0,0,0,0,0,1;
1,0,1;
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MAPLE
| g:=sum(t^(2*j-1)*x^(2*j-1)*product(1+x^(2*i-1), i=j+1..30), j=1..30): gser:=simplify(series(g, x=0, 52)): for n from 1 to 19 do P[n]:=sort(coeff(gser, x^n)) od: d:=proc(n) if n mod 2 = 1 then n elif n=2 then 0 elif n mod 4 = 0 then n/2-1 else n/2-2 fi end: 1; {}; for n from 3 to 19 do seq(coeff(P[n], t^j), j=1..d(n)) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A000700, A027349, A092319, A116857.
Sequence in context: A027345 A086080 A070139 * A179391 A083850 A028718
Adjacent sequences: A116857 A116858 A116859 * A116861 A116862 A116863
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KEYWORD
| nonn,tabf
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
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