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Search: id:A026807
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| A026807 |
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Triangular array T read by rows: T(n,k) = number of partitions of n in which every part is >=k, for k=1,2,...,n. |
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+0
6
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| 1, 2, 1, 3, 1, 1, 5, 2, 1, 1, 7, 2, 1, 1, 1, 11, 4, 2, 1, 1, 1, 15, 4, 2, 1, 1, 1, 1, 22, 7, 3, 2, 1, 1, 1, 1, 30, 8, 4, 2, 1, 1, 1, 1, 1, 42, 12, 5, 3, 2, 1, 1, 1, 1, 1, 56, 14, 6, 3, 2, 1, 1, 1, 1, 1, 1, 77, 21, 9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 101, 24, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 135, 34, 13
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OFFSET
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1,2
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COMMENT
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T(n,1)=A000041(n), T(n,2)=A002865(n) for n>1, T(n,3)=A008483(n) for n>2, T(n,4)=A008484(n) for n>3.
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FORMULA
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G.f.: Sum_{k>=1} y^k*(-1+1/Product_{i>=0} (1-x^(k+i))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 22 2003
T(n, k) = T(n, k+1)+T(n-k, k) (where T(n, n) = 1). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 24 2005
Equals A026794 * A000012 as infinite lower triangular matrices. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 31 2008
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EXAMPLE
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Sum_{k>=1} y^k*(-1+1/Product_{i>=0} (1-x^(k+i))) =
y*x+(2*y+y^2)*x^2+(3*y+y^2+y^3)*x^3+(5*y+2*y^2+y^3+y^4)*x^4+(7*y+2*y^2+y^3+y^4+y^5)*x^5+...
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CROSSREFS
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Row sums give A046746.
Cf. A026835.
Cf. A026794.
Sequence in context: A133913 A141412 A160183 this_sequence A106740 A110619 A129761
Adjacent sequences: A026804 A026805 A026806 this_sequence A026808 A026809 A026810
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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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