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Search: id:A073399
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| A073399 |
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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 A073400. |
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7
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| 1, 9, 30, 63, 531, 1050, 405, 6165, 29610, 44520, 2511, 59454, 502821, 1789614, 2245320, 15309, 517104, 6686631, 41182344, 120133692, 131891760, 92583, 4214349, 76790673, 714174327, 3559509360
(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^(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 q(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A073400(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; 9,30; 63,531,1050; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
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CROSSREFS
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Cf. A001045, A073370, A073400-A073402, A073372.
Sequence in context: A167154 A063150 A063161 this_sequence A005919 A084370 A000439
Adjacent sequences: A073396 A073397 A073398 this_sequence A073400 A073401 A073402
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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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