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Search: id:A113025
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| A113025 |
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Triangle of integer coefficients of polynomials P(n,x) of degree n arising in diagonal pade approximation of exp(x). |
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+0
2
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| 1, 1, 2, 1, 6, 12, 1, 12, 60, 120, 1, 20, 180, 840, 1680, 1, 30, 420, 3360, 15120, 30240, 1, 42, 840, 10080, 75600, 332640, 665280, 1, 56, 1512, 25200, 277200, 1995840, 8648640, 17297280, 1, 72, 2520, 55440, 831600, 8648640, 60540480, 259459200
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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exp(x) is well approximated by P(n,x)/P(n,-x) . (P(n,1)/P(n,-1))_{n>=0} is a sequence of convergents to e : i.e. P(n,1)=A001517(n) and P(n,-1)=abs(A002119(n))
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REFERENCES
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F. Wielonsky, Asymptotics of diagonal Hermite-Pade approximants to exp(x), J. Approx. Theory 90 (1997) 283-298.
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LINKS
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E. Weisstein, Pade approximants.
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FORMULA
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P(n, x)=sum(k=0, n, (n+k)!/k!/(n-k)!*x^(n-k))
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EXAMPLE
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P(3,x)=x^3+12*x^2+60*x+120
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PROGRAM
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(PARI) T(n, k)=(n+k)!/k!/(n-k)!
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CROSSREFS
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Adjacent sequences: A113022 A113023 A113024 this_sequence A113026 A113027 A113028
Sequence in context: A039795 A049949 A106192 this_sequence A113216 A081064 A128534
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KEYWORD
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nonn,tabl
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 03 2006
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