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A024200
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a(0) = 1, a(1) = 0, a(n+1) = 2*a(n) + (2*n-1)^2*a(n-1).
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3
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1, 0, 1, 2, 29, 156, 2661, 24198, 498105, 6440760, 156833865, 2638782090, 74441298645, 1544798322900, 49615408298925, 1225388793991950, 44177335967379825, 1265953302961023600, 50641025474398676625, 1652074847076051263250, 72631713568603890826125, 2658069269539881753055500
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OFFSET
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0,4
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COMMENTS
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a(n) = s(1)s(2)...s(n)(1/s(2) - 1/s(3) + ... + c/s(n)) where c=(-1)^n and s(k) = 2k-1 for k = 1,2,3,...
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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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LINKS
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FORMULA
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E.g.f.: (1-Pi/4)/sqrt(1-2*x) + 1/2*log(2*x+sqrt(4*x^2-1))/sqrt(2*x-1). - Vaclav Kotesovec, Mar 18 2014
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MATHEMATICA
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CoefficientList[Series[(1-Pi/4)/Sqrt[1-2*x] + 1/2*Log[2*x+Sqrt[4*x^2-1]]/Sqrt[2*x-1], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Mar 18 2014 *)
RecurrenceTable[{a[n+1] == 2*a[n] + (2*n-1)^2*a[n-1], a[0] == 1, a[1] == 0}, a, {n, 0, 20}] (* Vaclav Kotesovec, Mar 18 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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