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Search: id:A060063
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| A060063 |
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Triangle of coefficients of certain polynomials used for G.f.s of columns of triangle A060058. |
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+0
10
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| 1, 1, 1, 5, 26, 9, 61, 775, 1179, 225, 1385, 32516, 114318, 87156, 11025, 50521, 1894429, 11982834, 20371266, 9652725, 893025, 2702765, 148008446, 1472351967, 4417978068, 4546174779, 1502513550
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The row polynomials p(n,x) (rising powers of x) appear as numerators of the column G.f.s of triangle A060058.
First column (m=0) gives A000364 (Euler numbers). See A091742-4 for columns m=1..3.
The main diagonal gives A001818. The row sums give A052502. The alternating row sums give A091745.
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LINKS
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W. Lang, First 8 rows.
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FORMULA
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The row polynomials p(n, x) := sum(a(n, m)*x^m, m=0..n) satisfy the differential difference eq.: p(n, x)=x*((1-x)^2)*diff(p(n-1, x), x$2) + (1+6*(n-1)*x+(5-6*n)*x^2)*diff(p(n-1, x), x) + (3*n-2)*(1+(3*n-2)*x)*p(n-1, x), n>=1, with input p(0, x)=1. Added by W. Lang, Feb 13 2004.
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EXAMPLE
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{1}; {1,1}; {5,26,9}; {61,775,1179,225}; ... p(2,n)=5+26*x+9*x^2.
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CROSSREFS
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Adjacent sequences: A060060 A060061 A060062 this_sequence A060064 A060065 A060066
Sequence in context: A099077 A137113 A137115 this_sequence A106295 A057688 A048269
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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), Mar 16 2001
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