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Search: id:A089275
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| A089275 |
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Coefficient triangle of polynomials used for numerator of g.f.s for column sequences of array A078739. |
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+0
6
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| 1, 1, 18, 1, 118, 600, 1, 412, 11772, 35280, 1, 1060, 97308, 1494576, 3265920, 1, 2270, 508708, 23753736, 249815520, 439084800, 1, 4298, 1989148, 218417400, 6710001408, 54187574400, 80951270400, 1, 7448, 6355048, 1402502400
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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The polynomials are pe(n,x) := sum(a(n,m)*x^m,m=0..n-1). Companion polynomials are po(n,x) := sum(b(n,m)*x^m,m=0..n-1) with b(n,m) := A089276(n,m).
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LINKS
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W. Lang, First 7 rows, also for A089276.
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FORMULA
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Combined recursion for polynomials pe(n, x) and po(n, x) defined above: pe(n, x)= 2*(n-1)*po(n-1, x) + (1-(2*N-1)*(2*N-2)*x)*(pe(n-1, x)-2*(n-1)*po(n-1, x)) and po(n, x)= 2*(pe(n, x) + ((n-1)/2)*(1-2*n*(2*n-1)*x)*po(n-1, x))/(N+1).
Combined recursion with b(n, m) := A089276(n, m): a(n, m) = a(n-1, m) - 2*(2*n-1)*(n-1)*a(n-1, m-1) + 4*n*(2*n-1)*(n-1)*b(n-1, m-1) and b(n, m) = (-2*n*(2*n-1)*(n-1)*b(n-1, m-1) + (n-1)*b(n-1, m) + 2*a(n, m))/(n+1), with n>=m+1>=2 and a(1, 1)= 1 =b(1, 1), else 0.
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CROSSREFS
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Sequence in context: A040340 A040341 A111872 this_sequence A040319 A040318 A040320
Adjacent sequences: A089272 A089273 A089274 this_sequence A089276 A089277 A089278
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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_DOT_uni-karlsruhe_DOT_de), Nov 07 2003
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