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Search: id:A058405
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| A058405 |
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Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058404. |
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2
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| 2, 8, 20, 48, 288, 360, 320, 3520, 11360, 9840, 2176, 37888, 225344, 522752, 363360, 14848, 373504, 3491072, 14871296, 27849600, 16776000, 101376, 3467264, 46459904, 308703232, 1053556480, 1692808704, 922158720, 692224, 30834688
(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 P0(n) := A000129(n+1), n >= 0, (Pell numbers starting with P0(0)=1) with itself is Pk(n) := A054456(n+k,k) = (p(k-1,n)*(n+1)*2*P0(n+1) + q(k-1,n)*(n+2)*P0(n))/(k!*8^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)= A058404(k,m).
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LINKS
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W. Lang, First 7 rows, also for A058404.
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FORMULA
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Recursion for row polynomials defined in the comments: see A058402.
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EXAMPLE
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k=2: P2(n)=((8*n+22)*(n+1)*2*P0(n+1)+(8*n+20)*(n+2)*P0(n))/128, cf. A054457.
2; 8,20; 48,288,360; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0)
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CROSSREFS
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Cf. A000129, A054456, A058404, A054457, A058402-3 (rising powers).
Sequence in context: A131128 A066857 A146168 this_sequence A133326 A024997 A081157
Adjacent sequences: A058402 A058403 A058404 this_sequence A058406 A058407 A058408
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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), Dec 11 2000
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EXTENSIONS
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Link and cross-references added by Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 31 2002
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