OFFSET
0,2
COMMENTS
Binomial transform of A000557. - Vladimir Reshetnikov, Oct 29 2015
REFERENCES
Anthony G. Shannon and Richard L. Ollerton. "A note on Ledin's summation problem." The Fibonacci Quarterly 59:1 (2021), 47-56. See p. 49.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. R. J. Asveld & N. J. A. Sloane, Correspondence, 1987
P. R. J. Asveld, A family of Fibonacci-like sequences, Fib. Quart., 25 (1987), 81-83.
FORMULA
E.g.f.: exp(x)/(1-2*sinh(x)). - Sander Zwegers (s.zwegers(AT)hetnet.nl), Jun 28 2007
E.g.f.: 1/( U(0) -1 ) where U(k) = 1 + 1/(2^k - 2*x*4^k/(2*x*2^k - (k+1)/U(k+1) )); (continued fraction 3rd kind, 3-step ). - Sergei N. Gladkovskii, Dec 05 2012
a(n) ~ n! * phi / (sqrt(5) * (log(phi))^(n+1)), where phi is the golden ratio. - Vaclav Kotesovec, Nov 27 2017
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k + 1) * binomial(n,k) * (2^k + 1) * a(n-k). - Ilya Gutkovskiy, Jan 16 2020
MATHEMATICA
Round@Table[Sum[Binomial[n, k] (-1)^k (PolyLog[-k, 1-GoldenRatio] - PolyLog[-k, GoldenRatio])/Sqrt[5] , {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 29 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Nov 23 2001
STATUS
approved