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 A001569 Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*(1-exp(x))^(1/2)). (Formerly M2161 N0861) 8
 1, -1, -1, 2, 37, 329, 1501, -31354, -1451967, -39284461, -737652869, 560823394, 1103386777549, 82520245792997, 4398448305245905, 168910341581721494, 998428794798272641, -720450682719825322809, -105099789680808769094057, -10594247095804692725600734 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES 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). LINKS Table of n, a(n) for n=0..19. S. M. Kerawala, Asymptotic solution of the "Probleme des menages, Bull. Calcutta Math. Soc., 39 (1947), 82-84. [Annotated scanned copy] FORMULA 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 MATHEMATICA m = 20; B[x_] = BesselI[0, x] + O[x]^(2 m) // Normal; A[x_] = B[2(1 - E^x)^(1/2)] + O[x]^m; CoefficientList[A[x], x]*Range[0, m-1]!^2 (* Jean-François Alcover, Oct 26 2019 *) PROG (PARI) a(n)=n!*sum(k=0, n, (-1)^k*stirling(n, k, 2)/k!) \\ Charles R Greathouse IV, Apr 18 2016 CROSSREFS Sequence in context: A078976 A200911 A243101 * A092853 A297796 A300542 Adjacent sequences: A001566 A001567 A001568 * A001570 A001571 A001572 KEYWORD sign,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Vladeta Jovovic, Jul 17 2006 STATUS approved

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)