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Search: id:A033842
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| A033842 |
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Triangle of coefficients of certain polynomials (exponents in decreasing order). |
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12
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| 1, 1, 1, 3, 3, 1, 16, 16, 6, 1, 125, 125, 50, 10, 1, 1296, 1296, 540, 120, 15, 1, 16807, 16807, 7203, 1715, 245, 21, 1, 262144, 262144, 114688, 28672, 4480, 448, 28, 1, 4782969, 4782969, 2125764, 551124, 91854, 10206, 756, 36, 1, 100000000
(list; table; graph; listen)
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OFFSET
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0,4
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LINKS
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W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
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a(n, m) = binomial(n+1, m)*(n+1)^(n-m-1), n >= m >= 0 else 0.
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EXAMPLE
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{1}; {1,1}; {3,3,1}; {16,16,6,1}; {125,125,50,10,1}; .... E.g. third row {3,3,1} corresponds to polynomial p{3,x)= 3*x^2+3*x+1.
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CROSSREFS
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a(n, 0)= A000272(n+1), n >= 0 (first column), a(n, 1)= A000272(n+1), n >= 1 (second column). p(k-1, -x)/(1-k*x)^k = (-1+1/(1-k*x)^k)/(x*k^2) is for k=1..5 G.f. for A000012, A001792, A036068, A036070, A036083, respectively.
See also A049323.
Sequence in context: A123244 A105599 A106210 this_sequence A104417 A121438 A108391
Adjacent sequences: A033839 A033840 A033841 this_sequence A033843 A033844 A033845
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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)
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