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Search: id:A024199
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| A024199 |
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a(0) = 0, a(1) = 1, a(n+1) = 2*a(n) + (2*n-1)^2*a(n-1). |
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+0
5
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| 0, 1, 2, 13, 76, 789, 7734, 110937, 1528920, 28018665, 497895210, 11110528485, 241792844580, 6361055257725, 163842638377950, 4964894559637425, 147721447995130800, 5066706567801827025, 171002070002301095250, 6548719685561840296125, 247199273204273879989500
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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A. E. Jolliffe, Continued Fractions, in Encyclopaedia Britannica, 11th ed., pp. 30-33; see p. 31.
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FORMULA
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a(n) = s(1)s(2)...s(n)(1/s(1) - 1/s(2) + ... + c/s(n)) where c=(-1)^(n+1) and s(k) = 2k-1 for k = 1, 2, 3, ...
A024199(n) + A024200(n) = A001147(n) = (2n-1)!! - Max Alekseyev (maxal(AT)cs.ucsd.edu), Sep 23 2007.
A024199(n)/A024200(n) -> Pi/(4-Pi) as n -> oo. - Max Alekseyev (maxal(AT)cs.ucsd.edu), Sep 23 2007.
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MAPLE
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f := proc(n) option remember; local a, b, t1, t2, t3, i, j, k; a := 0; b := 1; if n=0 then RETURN(a) elif n=1 then RETURN(b) else RETURN(2*f(n-1)+ (2*n-3)^2*f(n-2)); fi; end;
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CROSSREFS
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Cf. A004041.
Sequence in context: A004027 A007509 A077413 this_sequence A037523 A037732 A090187
Adjacent sequences: A024196 A024197 A024198 this_sequence A024200 A024201 A024202
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by njas, Jul 19 2002.
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