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Search: id:A103360
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| A103360 |
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Denominator of coefficient in the interpolation polynomial for initial values of the factorial, read by row. |
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+0
5
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| 1, 1, 1, 2, 2, 1, 3, 2, 6, 1, 8, 12, 8, 12, 1, 30, 24, 12, 24, 60, 1, 144, 240, 144, 48, 36, 20, 1, 280, 720, 240, 144, 240, 180, 140, 1, 5760, 10080, 960, 180, 640, 1440, 1440, 280, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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N(n,n)/D(n,n) = Sum{k=0..n}(-1)^k/k! = A000166/n! = A053557/A053556, where N(n,n) is A103361.
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FORMULA
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D(n, k) in Sum{k=0..n}N(n, k)/D(n, k)*m^k=m!, m=0..n, with reduced fraction N(n, k)/D(n, k) and N(n, k) is A103361. D(n, k)=a(n*(n+3)/2-k).
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EXAMPLE
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1; 1; 1/2*x^2-1/2*x+1; 1/3*x^3-1/2*x^2+1/6*x+1;
3/8*x^4-23/12*x^3+29/8*x^2-25/12*x+1;
11/30*x^5-79/24*x^4+131/12*x^3-353/24*x^2+403/60*x+1
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CROSSREFS
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Cf. A103361, A000166, A053556, A053557.
Sequence in context: A129711 A030454 A145141 this_sequence A104469 A144112 A104660
Adjacent sequences: A103357 A103358 A103359 this_sequence A103361 A103362 A103363
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KEYWORD
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easy,frac,nonn,tabl
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AUTHOR
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Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Feb 02 2005
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