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A069943
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a(n) = numerator(b(n)), where b(1) = b(2) = 1, b(n) = (b(n-1) + b(n-2))/(n-1).
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3
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1, 1, 1, 2, 5, 13, 19, 29, 191, 131, 1187, 2231, 17519, 71063, 29881, 323423, 2887921, 13237457, 2397389, 15030317, 742458253, 3748521653, 9670072483, 25451905333, 10932619111, 78684575461, 4163946939067, 11799518538967, 136025604432743
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OFFSET
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1,4
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COMMENTS
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Sum_{k>=1} b(k) = exp(3/2). More generally if b(1) = b(2) = ... = b(m) = 1 and b(n+m+1) = (1/(n+m))*(b(n+m) + b(n+m-1) + ... + b(n)) then Sum_{k>=1} b(k) = exp(H(m)) where H(m) = Sum_{j=1..m} 1/j is the m-th harmonic number. [Benoit Cloitre and Boris Gourevitch]
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LINKS
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FORMULA
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Numerators in the power series of exp(x+x^2/2) (e.g.f. for involutions, cf. A000085). exp(x+x^2/2) = 1 + x + x^2 + 2/3*x^3 + 5/12*x^4 + 13/60*x^5 + 19/180*x^6 + 29/630*x^7 + 191/10080*x^8 + ... [Joerg Arndt, May 10 2008]
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MATHEMATICA
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Table[Numerator[n*(-I/Sqrt[2])^(n-1)*HermiteH[n-1, I/Sqrt[2]]/n!], {n, 40}] (* G. C. Greubel, Aug 17 2022 *)
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PROG
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(Magma)
A013989:= func< n | (&+[Factorial(n)/(2^k*Factorial(n-2*k)*Factorial(k)): k in [0..Floor(n/2)]]) >;
(SageMath)
@CachedFunction
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CROSSREFS
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KEYWORD
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easy,frac,nonn
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AUTHOR
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STATUS
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approved
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