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Search: id:A055864
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| A055864 |
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Coefficient triangle for certain polynomials. |
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+0
7
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| 1, 3, 2, 16, 12, 9, 125, 100, 80, 64, 1296, 1080, 900, 750, 625, 16807, 14406, 12348, 10584, 9072, 7776, 262144, 229376, 200704, 175616, 153664, 134456, 117649, 4782969, 4251528, 3779136, 3359232, 2985984, 2654208, 2359296, 2097152
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The coefficients of the partner polynomials are found in triangle A055858.
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FORMULA
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a(n, m)=0 if n<m; a(n, m)= n^(m-1)*(n+1)^(n-m), n >= m >= 1;
E.g.f. for column m: A(m, x); A(1, x)=-(W(-x)/x+1); recursion: A(m, x) = A(m-1, x)-int(A(m-1, x), x)/x-(((m-1)^(m-1))/m)* (x^(m-1))/(m-1)!, m >= 2; W(x) principal branch of Lambert's function.
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EXAMPLE
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{1}; {3,2}; {16,12,9}; {125,100,80,64};...
Fourth row polynomial (n=4): p(4,x)= 125+100*x+80*x^2+64*x^3
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CROSSREFS
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Column sequences are: A000272(n+1), n >= 1, A055865, A055070, A055867, A055868 for m=1..5.
Adjacent sequences: A055861 A055862 A055863 this_sequence A055865 A055866 A055867
Sequence in context: A111999 A126323 A084886 this_sequence A072045 A126354 A026345
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 20 2000
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