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Search: id:A060098
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| A060098 |
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Triangle of partial sums of column sequences of triangle A060086. |
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+0
6
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| 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 8, 4, 1, 1, 9, 16, 13, 5, 1, 1, 12, 30, 32, 19, 6, 1, 1, 16, 50, 71, 55, 26, 7, 1, 1, 20, 80, 140, 140, 86, 34, 8, 1, 1, 25, 120, 259, 316, 246, 126, 43, 9, 1, 1, 30, 175, 448, 660, 622, 399
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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In the language of the Shapiro et al. reference (given in A053121) such a lower triangular (ordinary) convolution array, considered as a matrix, belongs to the Riordan-group. The G.f. for the row polynomials p(n,x)= sum(a(n,m)*x^m,m=0..n) is (1/(1-x*z/((1-z^2)*(1-z))))/(1-z).
Row sums give A052534. Column sequences (without leading zeros) give A000012 (powers of 1), A002620(n+1), A002624, A060099-A060101 for m=0..5.
The bisections of the column sequences give triangles A060102 and A060556.
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FORMULA
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G.f. for column m >= 0: ((x/((1-x^2)*(1-x)))^m)/(1-x)= x^m/((1+x)^m*(1-x)^(2*m+1)).
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EXAMPLE
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{1}; {1,1}; {1,2,1}; {1,4,3,1}; ...; p(3,x)=1+4*x+3*x^2+x^3.
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CROSSREFS
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Sequence in context: A130523 A034363 A026769 this_sequence A034781 A110470 A055080
Adjacent sequences: A060095 A060096 A060097 this_sequence A060099 A060100 A060101
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 06 2001
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