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Search: id:A122075
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| A122075 |
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Coefficients of a generalized Pell-Lucas polynomial read by rows. |
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+0
2
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| 1, 2, 1, 3, 3, 1, 5, 7, 4, 1, 8, 15, 12, 5, 1, 13, 30, 31, 18, 6, 1, 21, 58, 73, 54, 25, 7, 1, 34, 109, 162, 145, 85, 33, 8, 1, 55, 201, 344, 361, 255, 125, 42, 9, 1, 89, 365, 707, 850, 701, 413, 175, 52, 10, 1, 144, 655, 1416, 1918, 1806, 1239, 630, 236, 63, 11, 1
(list; table; graph; listen)
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OFFSET
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1,2
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LINKS
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Y. Sun, Numerical Triangles and Several Classical Sequences, Fib. Quart. 43, no. 4, (2005) 359-370.
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FORMULA
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T(n,k)=sum_(j=0..n-k+1) binomial(n-k-j+1,j)*binomial(n-j,k). sum_(k>=0) T(n-k,k)=2^n. sum_(k>=0) (-1)^k T(n-k,k)=2-delta(0,n).
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EXAMPLE
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1
2 1
3 3 1
5 7 4 1
8 15 12 5 1
13 30 31 18 6 1
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PROGRAM
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(PARI) T(n, k)={ sum(j=0, n-k+1, binomial(n-k-j+1, j)*binomial(n-j, k)) ; } { nmax=10 ; for(n=0, nmax, for(k=0, n, print1(T(n, k), ", ") ; ); ); }
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CROSSREFS
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Adjacent sequences: A122072 A122073 A122074 this_sequence A122076 A122077 A122078
Sequence in context: A048600 A100578 A061315 this_sequence A127119 A066704 A127123
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2006
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