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Search: id:A026821
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| A026821 |
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Triangular array T read by rows: T(n,k) = number of partitions of n into distinct parts, the least being k, for k=1,2,...,n. |
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1
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| 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 1, 3, 2, 1, 1, 0, 0, 0, 0, 1, 5, 2, 1, 1, 0, 0, 0, 0, 0, 1, 5, 3, 1, 1, 1, 0, 0, 0, 0, 0, 1, 7, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 8, 4, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,16
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COMMENT
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T(n,1)=A025147(n-1). Sum(k*T(n,k),k=1..n)=A092265(n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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FORMULA
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T(n, k) = T(n-k, k+1) + ... + T(n-k, n-k) for 1<=k<=m and T(n, k)=0 for m+1<=k<=n-1, where m=[ (n-1)/2 ]; T(n, n)=1 for n >= 1.
G.f.=sum(t^j*x^j*product(1+x^i,i=j+1..infinity),j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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EXAMPLE
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T(11,2)=3 because we have [9,2],[6,3,2] and [5,4,2].
Triangle starts:
1;
0,1;
1,0,1;
1,0,0,1;
1,1,0,0,1;
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MAPLE
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g:=sum(t^j*x^j*product(1+x^i, i=j+1..50), j=1..50): gser:=simplify(series(g, x=0, 18)): for n from 1 to 14 do P[n]:=sort(coeff(gser, x^n)) od: seq(seq(coeff(P[n], t^j), j=1..n), n=1..14); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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CROSSREFS
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Cf. A025147, A092265.
Sequence in context: A024944 A117907 A103633 this_sequence A039964 A035172 A110174
Adjacent sequences: A026818 A026819 A026820 this_sequence A026822 A026823 A026824
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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