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Search: id:A073401
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| A073401 |
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Coefficient triangle of polynomials (rising powers) related to convolutions of A001045(n+1), n>=0, (generalized (1,2)-Fibonacci). Companion triangle is A073402. |
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+0
4
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| 1, 30, 9, 1050, 531, 63, 44520, 29610, 6165, 405, 2245320, 1789614, 502821, 59454, 2511, 131891760, 120133692, 41182344, 6686631, 517104, 15309, 8862693840, 8966770308, 3559509360, 714174327
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The row polynomials are p(k,x) := sum(a(k,m)*x^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 q(k,n) := sum(b(k,m)*n^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A073402(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: p(k, n)= (n+2)*p(k-1, n+1)+4*(n+2*(k+1))*p(k-1, n)+2*(n+3)*q(k-1, n); q(k, n)= (n+1)*p(k-1, n+1)+4*(n+2*(k+1))*q(k-1, n), k >= 1.
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EXAMPLE
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k=2: U2(n)=((30+9*n)*(n+1)*U0(n+1)+(33+9*n)*(n+2)*2*U0(n))/(2*9^2), cf. A073372.
1; 30,9; 1050,531,63; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
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CROSSREFS
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Cf. A001045, A073370, A073399, A073372, A073402, A073400.
Sequence in context: A040879 A040877 A040876 this_sequence A040875 A131773 A091746
Adjacent sequences: A073398 A073399 A073400 this_sequence A073402 A073403 A073404
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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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