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Search: id:A078801
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| A078801 |
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Expansion of gaussian product of arithmetic mean and Lehmer mean evaluated at 1+4x. |
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+0
1
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| 1, 2, 2, -4, 10, -28, 76, -184, 378, -620, 708, -328, -36, -4008, 25960, -83984, 135066, 188788, -2232236, 9070040, -23335660, 29933128, 69732568, -630906096, 2551027132, -7193660232, 13576199192, -5110303664, -92186317112
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 265-266, Exercise 7.
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FORMULA
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G.f.: A(x) satisfies A(x)=(1+2x)A(x^2/(1+2x)^2), A(0)=1.
a(n)=(-1)^n sum_{k>0} 2^(n-2k)a(k)binomial(n-2, n-2k), n>1.
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PROGRAM
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(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=(1+2*x)*subst(A, x, x^2/(1+2*x)^2)); polcoeff(A, n))
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CROSSREFS
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Sequence in context: A100088 A025244 A132824 this_sequence A002420 A112556 A054100
Adjacent sequences: A078798 A078799 A078800 this_sequence A078802 A078803 A078804
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KEYWORD
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sign,easy
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AUTHOR
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Michael Somos, Dec 05, 2002
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