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Search: id:A057995
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| A057995 |
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Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057280. |
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+0
5
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| 1, 16, 5, 300, 160, 20, 6840, 4850, 1075, 75, 186120, 159650, 48175, 6100, 275, 5916240, 5846700, 2168650, 379700, 31550, 1000, 215717040, 238437900, 103057800, 22426825, 2605175, 153875, 3625, 8888140800, 10772348400
(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 F0(n) := A000045(n+1) n >= 0, (Fibonacci starting with F0(0)=1) with itself is Fk(n) := A037027(n+k,k) = (p(k-1,n)*(n+1)*F0(n+1) + q(k-1,n)*(n+2)*F0(n))/(k!*5^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)= A057280).
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EXAMPLE
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k=2: F2(n)=((16+5*n)*(n+1)*F0(n+1)+(17+5*n)*(n+2)*F0(n))/50, cf. A001628.
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CROSSREFS
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Cf. A000045, A037027, A057280.
Sequence in context: A040245 A070538 A070581 this_sequence A097533 A040244 A084527
Adjacent sequences: A057992 A057993 A057994 this_sequence A057996 A057997 A057998
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KEYWORD
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nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2000
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