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Search: id:A062134
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| A062134 |
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Triangle of coefficients of polynomials (rising powers) useful for convolutions of A001333(n+1), n >= 0 (associated Pell numbers). |
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+0
2
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| 1, 2, 0, 8, 24, 16, 336, 832, 576, 128, 12480, 28480, 23680, 8960, 1280, 481920, 1208832, 1167360, 552960, 130560, 12288, 22786560, 61834752, 65709056, 35911680, 10895360, 1763328, 118784, 1280885760, 3645444096
(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 pPL1(n,x) := sum(A062133(n,m)*x^m,m=0..n) and pPL2(n,x) := sum(a(n,m)*x^m,m=0..n) appear in the k-fold convolution of the associated Pell numbers PL(n) := A001333(n+1), n >= 0, as follows: PL(k; n) := A054458(n+k,k)= (2*pPL1(k,n)*PL(n+1)+pPL2(k,n)*PL(n)/(k!*8^k), k >= 0.
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EXAMPLE
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{1}; {2,0}; {8,24,16}; {336,832,576,128}; ...
pPL1(1,n)=1+2*n; pL2(1,n)=2; PL(1; n)= A054459(n)=((1+2*n)*PL(n+1)+PL(n))/4.
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CROSSREFS
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A062133(n, m) (companion triangle), A054458(n, m) (convolution triangle).
Sequence in context: A120555 A128063 A087205 this_sequence A002909 A118437 A134185
Adjacent sequences: A062131 A062132 A062133 this_sequence A062135 A062136 A062137
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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), Jun 19 2001
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