OFFSET
0,4
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..250
C. Banderier, H.-K. Hwang, V. Ravelomanana and V. Zacharovas, Analysis of an exhaustive search algorithm in random graphs and the n^{c logn}-asymptotics, SIAM J. Discrete Math., 28(1), 342-371. (30 pages), DOI:10.1137/130916357. - From N. J. A. Sloane, Dec 23 2012
Peter C. Fishburn, Peter C. Marcus-Roberts, Fred S. Roberts, Unique finite difference measurement, SIAM J. Discrete Math. 1 (1988), no. 3, 334-354.
P. C. Fishburn, A. M. Odlyzko and F. S. Roberts, 2-sided generalized Fibonacci sequences, Fib. Quart., 27 (1989), 352-361.
Rui-Li Liu, Feng-Zhen Zhao, New Sufficient Conditions for Log-Balancedness, With Applications to Combinatorial Sequences, J. Int. Seq., Vol. 21 (2018), Article 18.5.7.
Poloni, Federico; Del Corso, Gianna M. Counting Fiedler pencils with repetitions. Linear Algebra Appl. 532, 463-499 (2017).
FORMULA
If n <= 2 then a(n) = 1 otherwise a(n) = 2*(n-1)*a(n-1)-(n-2)^2*a(n-2).
E.g.f.: (e*Ei(1/(x-1)) - e*Ei(-1)-1)/(e^(x/(x-1))*(x-1)), where Ei is the exponential integral function. - Jean-François Alcover, Sep 05 2015, after Fishburn et al.
0 = a(n)*(-24*a(n+2) + 99*a(n+3) - 78*a(n+4) + 17*a(n+5) - a(n+6)) + a(n+1)*(-15*a(n+2) + 84*a(n+3) - 51*a(n+4) + 6*a(n+5)) + a(n+2)*(-6*a(n+2) + 34*a(n+3) - 15*a(n+4)) + a(n+3)*(+10*a(n+3)) for all n in Z. - Michael Somos, Dec 02 2016
EXAMPLE
G.f. = 1 + x + x^2 + 3*x^3 + 14*x^4 + 85*x^5 + 626*x^6 + 5387*x^7 + ...
MAPLE
A005189 :=proc(n) option remember;
if n <= 2 then 1 else 2*(n-1)*procname(n-1)-(n-2)^2*procname(n-2); fi; end;
[seq(A005189(n), n=0..20)]; # N. J. A. Sloane, Jul 10 2015
MATHEMATICA
$Assumptions = Element[x, Reals]; F[x_] := (E*ExpIntegralEi[1/(x-1)] - E*ExpIntegralEi[-1]-1)/(E^(x/(x-1))*(x-1)); Join[{1}, CoefficientList[ Normal[Series[F[x], {x, 0, 18}]], x]*Range[0, 18]!] (* Jean-François Alcover, Sep 05 2015 *)
PROG
(PARI) {a(n) = if(n<3, n>=0, 2*(n-1)*a(n-1) - (n-2)^2*a(n-2))}; /* Michael Somos, Dec 02 2016 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Sep 05 2005
STATUS
approved