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Search: id:A055858
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| A055858 |
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Coefficient triangle for certain polynomials. |
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+0
12
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| 1, 1, 2, 4, 9, 6, 27, 64, 48, 36, 256, 625, 500, 400, 320, 3125, 7776, 6480, 5400, 4500, 3750, 46656, 117649, 100842, 86436, 74088, 63504, 54432, 823543, 2097152, 1835008, 1605632, 1404928, 1229312, 1075648, 941192, 16777216, 43046721
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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The coefficients of the partner polynomials are found in triangle A055864.
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FORMULA
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a(n, m)=0 if n<m; a(0, 0)=1, a(n, 0)= n^n, n >= 1, a(n, m)= n^(m-1)*(n+1)^(n-m+1), n >= m >= 1;
E.g.f. for column m: A(m, x); A(0, x)= 1/(1+W(-x)); A(1, x)= -1-diff(W(-x), x) = -1-W(-x)/((1+W(-x))*x); A(2, x)=A(1, x)-int(A(1, x), x)/x-(1/x+x); recursion: A(m, x) = A(m-1, x)-int(A(m-1, x), x)/x-((m-1)^(m-1))*(x^(m-1))/(m-1)!, m >= 3; W(x) principal branch of Lambert's function.
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EXAMPLE
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{1}; {1,2}; {4,9,6}; {27,64,48,36};...
Fourth row polynomial (n=3): p(3,x)= 27+64*x+48*x^2+36*x^3
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CROSSREFS
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Column sequences are A000312(n), n >= 1, A055860 (A000169), A055861 (A053506), A055862-3 for m=0..4, row sums: A045531(n+1)= |A039621(n+1, 2)|, n >= 0.
Sequence in context: A104654 A011182 A063507 this_sequence A141389 A133757 A076125
Adjacent sequences: A055855 A055856 A055857 this_sequence A055859 A055860 A055861
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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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