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Search: id:A058404
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| A058404 |
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Coefficient triangle of polynomials (falling powers) related to Pell number convolutions. Companion triangle is A058405. |
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4
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| 1, 8, 22, 56, 376, 588, 384, 4576, 17024, 19656, 2624, 48256, 313504, 848096, 801360, 17920, 468608, 4643072, 21685888, 47494272, 38797920, 122368, 4307456, 60136448, 424509952, 1590913920, 2986217856, 2181332160, 835584, 38055936
(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 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 q(k,n) := sum(b(k,m)*n^(k-m),m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A058405(k,m).
a(k,0)= A057084(k), k >= 0 (conjecture).
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LINKS
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W. Lang, First 7 rows, also for A058405.
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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.
1; 8,22; 56,376,588; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0)
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CROSSREFS
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Cf. A000129, A054456, A058405, A054457, A057084, A058402-3 (rising powers).
Sequence in context: A048489 A124701 A002968 this_sequence A126362 A140418 A083098
Adjacent sequences: A058401 A058402 A058403 this_sequence A058405 A058406 A058407
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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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