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Search: id:A103361
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| A103361 |
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Numerator of coefficient in the interpolation polynomial for initial values of the factorial, read by rows. |
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+0
5
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| 1, 0, 1, 1, -1, 1, 1, -1, 1, 1, 3, -23, 29, -25, 1, 11, -79, 131, -353, 403, 1, 53, -1237, 4031, -3451, 3101, -749, 1, 103, -5297, 14213, -34903, 126121, -101297, 31837, 1, 2199, -100123, 106657, -119129, 1438599, -6199951, 6112397, -455481, 1
(list; table; graph; listen)
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OFFSET
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0,11
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COMMENT
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Denominator N(n,n) of leading coefficient of the n-th polynomial = n-th term of A053557. N(n,n)/D(n,n) = Sum{k=0..n}(-1)^k/k! = A000166/n! = A053557/A053556, where D(n,n) is A103360.
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FORMULA
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N(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 D(n, k) is A103360. N(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. A103360, A000166, A053556, A053557.
Sequence in context: A153834 A153707 A153708 this_sequence A136090 A032688 A142345
Adjacent sequences: A103358 A103359 A103360 this_sequence A103362 A103363 A103364
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KEYWORD
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easy,frac,sign,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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