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 A005444 From a Fibonacci-like differential equation. (Formerly M2766) 2
 1, 1, 3, 8, 50, 214, 2086, 11976, 162816, 1143576, 20472504, 165910128, 3785092032, 33908109936, 967508478192, 9252123203712, 327062428940160, 3236057604910080, 141403289873955840, 1404243298160352000, 76168955916831029760, 735206146073008508160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence is signed: first negative term is a(35) = -230450728485788167742674544892530875760640. - Vladeta Jovovic, Sep 29 2003 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Georg Fischer, Table of n, a(n) for n = 0..100 P. R. J. Asveld & N. J. A. Sloane, Correspondence, 1987 P. R. J. Asveld, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309. FORMULA a(n) = Sum(k!*fibonacci(k + 1)*stirling1(n, k), k = 0..n). E.g.f.: 1/(1-log(1+x)-log(1+x)^2). - Vladeta Jovovic, Sep 29 2003 a(n) ~ n! * (-1)^n * exp(n*(1+sqrt(5))/2) / (sqrt(5)*(exp((1+sqrt(5))/2)-1)^(n+1)). - Vaclav Kotesovec, Oct 01 2013 MATHEMATICA CoefficientList[Series[1/(1-Log[1+x]-(Log[1+x])^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *) PROG (PARI) a(n) = sum(k=0, n, k!*fibonacci(k+1)*stirling(n, k, 1)); \\ Michel Marcus, Oct 30 2015 CROSSREFS Sequence in context: A000862 A306042 A194364 * A222684 A208801 A019044 Adjacent sequences:  A005441 A005442 A005443 * A005445 A005446 A005447 KEYWORD sign,easy AUTHOR STATUS approved

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Last modified May 27 03:03 EDT 2020. Contains 334647 sequences. (Running on oeis4.)