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Search: id:A073400
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| A073400 |
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Coefficient triangle of polynomials (falling powers) related to convolutions of A001045(n+1), n>=0, (generalized (1,2)-Fibonacci). Companion triangle is A073399. |
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7
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| 2, 9, 33, 45, 396, 831, 243, 3744, 18297, 28236, 1377, 32481, 273483, 968679, 1210140, 8019, 268029, 3418767, 20681811, 58920534, 62686440, 47385, 2130138, 38186478, 347584284, 1683064737, 4075425738
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..
The k-th convolution of U0(n) := A001045(n+1), n>= 0, ((1,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073370(n+k,k) = (p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*2*U0(n))/(k!*9^k), k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A073399(k,m).
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LINKS
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W. Lang First 7 rows .
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FORMULA
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Recursion for row polynomials defined in the comments: see A073401.
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EXAMPLE
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k=2: U2(n)=((9*n+30)*(n+1)*U0(n+1)+(9*n+33)*(n+2)*2*U0(n))/(2*9^2), cf. A073372.
1; 9,33; 45,396,831; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
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CROSSREFS
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Cf. A001045, A073370, A073399, A073401.
Sequence in context: A139628 A123142 A122097 this_sequence A048498 A150921 A150922
Adjacent sequences: A073397 A073398 A073399 this_sequence A073401 A073402 A073403
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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), Aug 2, 2002
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