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A001569
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Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*(1-exp(x))^(1/2)).
(Formerly M2161 N0861)
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8
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1, -1, -1, 2, 37, 329, 1501, -31354, -1451967, -39284461, -737652869, 560823394, 1103386777549, 82520245792997, 4398448305245905, 168910341581721494, 998428794798272641, -720450682719825322809, -105099789680808769094057, -10594247095804692725600734
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OFFSET
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0,4
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REFERENCES
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S. M. Kerawala, Asymptotic solution of the "Probleme des menages", Bull. Calcutta Math. Soc., 39 (1947), 82-84.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Let b(n) satisfy (n-2)*b(n) - n*(n-2)*b(n-1) - n*b(n-2) = 0; write b(n) = (n!/e^2)*(1 + Sum_{r>=1} a_r/n^r).
a(n) = n!*Sum_{k=0..n} (-1)^k*Stirling2(n,k)/k!. - Vladeta Jovovic, Jul 17 2006
E.g.f.: 1 + x*(1 - E(0))/(1-x) where E(k) = 1 + 1/(1-x*(k+1))/(k+1)/(1-x/(x-1/E(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 19 2013
E.g.f.: 1 + x*(1 - S)/(1-x) where S = Sum_{k>=0} (1 + 1/(1-x-x*k)/(k+1)) * x^k / Product_{i=0..k-1} (1-x-x*i)*(i+1). - Sergei N. Gladkovskii, Jan 21 2013
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MATHEMATICA
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m = 20;
B[x_] = BesselI[0, x] + O[x]^(2 m) // Normal;
A[x_] = B[2(1 - E^x)^(1/2)] + O[x]^m;
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PROG
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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