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Search: id:A058403
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| A058403 |
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Coefficient triangle of polynomials (rising powers) related to Pell number convolutions. Companion triangle is A058402. |
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+0
4
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| 2, 20, 8, 360, 288, 48, 9840, 11360, 3520, 320, 363360, 522752, 225344, 37888, 2176, 16776000, 27849600, 14871296, 3491072, 373504, 14848, 922158720, 1692808704, 1053556480, 308703232, 46459904, 3467264, 101376, 58499239680, 115821927936
(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^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^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A058402(k,m).
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LINKS
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W. Lang, First 7 rows, also for A058402.
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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)=((22+8*n)*(n+1)*2*P0(n+1)+(20+8*n)*(n+2)*P0(n))/128, cf. A054457.
2; 20,8; 360,288,48; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).
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CROSSREFS
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Cf. A000129, A054456, A058402, A058404-5 (falling powers).
Sequence in context: A077339 A077341 A076495 this_sequence A083297 A012739 A075031
Adjacent sequences: A058400 A058401 A058402 this_sequence A058404 A058405 A058406
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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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