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Search: id:A073404
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| A073404 |
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Coefficient triangle of polynomials (falling powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073403. |
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3
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| 2, 12, 36, 96, 672, 1056, 864, 10752, 40416, 43968, 8064, 156672, 1051776, 2815488, 2396160, 76032, 2121984, 22125312, 105981696, 226492416, 161879040, 718848, 27205632, 404656128, 2995605504
(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) := A002605(n), n>= 0, ((2,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073387(n+k,k) = 2*(p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*U0(n))/(k!*(2^2+4*2)^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)= A073403(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 A073405.
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EXAMPLE
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k=2: U2(n)=(2*(36+12*n)*(n+1)*U0(n+1)+2*(36+12*n)*(n+2)*U0(n))/(2!*12^2), cf. A073389.
1; 12,36; 96,672,1056; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
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CROSSREFS
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Cf. A002605, A073387, A073403, A073405.
Adjacent sequences: A073401 A073402 A073403 this_sequence A073405 A073406 A073407
Sequence in context: A055699 A062094 A011379 this_sequence A141208 A035597 A000913
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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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