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 A005445 From a Fibonacci-like differential equation. (Formerly M4487) 6
 0, 1, 1, 8, 16, 224, 608, 13320, 41760, 1366152, 4440312, 215100192, 655723440, 48242081328, 121651212720, 14627299801728, 24367884018048, 5768946415383552, 2780730890516736, 2872938805170308352, -2941729703083507968, 1764460446550873413120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..434 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 From Vladeta Jovovic, Sep 29 2003: (Start) a(n) = Sum_{k=0..n} Stirling1(n, k)*k!*Fibonacci(k). E.g.f.: log(1+x)/(1 - log(1+x) - log(1+x)^2). (End) a(n) ~ n! * (-1)^(n+1) * (1+1/sqrt(5)) * exp(n*(1+sqrt(5))/2) /(2*(exp((1+sqrt(5))/2)-1)^(n+1)). - Vaclav Kotesovec, Oct 01 2013 MATHEMATICA CoefficientList[Series[Log[1+x]/(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)*stirling(n, k, 1)); \\ Michel Marcus, Oct 30 2015 (Magma) [(&+[Factorial(j)*Fibonacci(j)*StirlingFirst(n, j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Nov 21 2022 (SageMath) def A005445(n): return sum((-1)^(n+k)*factorial(k)*fibonacci(k)* stirling_number1(n, k) for k in range(n+1)) [A005445(n) for n in range(31)] # G. C. Greubel, Nov 21 2022 CROSSREFS Cf. A000045, A000142, A005444, A048994, A320352. Sequence in context: A061359 A330150 A340586 * A322342 A132377 A276978 Adjacent sequences: A005442 A005443 A005444 * A005446 A005447 A005448 KEYWORD sign AUTHOR Simon Plouffe EXTENSIONS More terms from Vladeta Jovovic, Sep 29 2003 STATUS approved

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Last modified September 12 12:03 EDT 2024. Contains 375851 sequences. (Running on oeis4.)