OFFSET
1,2
COMMENTS
Equals the eigensequence of an infinite lower triangular matrix with 1's in the main diagonal and the triangular series in the subdiagonal.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
E.g.f.: -2*exp(sqrt(2)*arctanh(x/sqrt(2)))/(x^2-2) = ((sqrt(2) + x)^2/(2 - x^2))^(1/sqrt(2))*2/(2 - x^2). - Vaclav Kotesovec, Oct 19 2012
a(n) ~ n!*2^(1/sqrt(2)-n/2)*n^(1/sqrt(2))/(2*Gamma(1+1/sqrt(2))). - Vaclav Kotesovec, Oct 19 2012
MATHEMATICA
Rest[CoefficientList[Series[-2*E^(Sqrt[2]*ArcTanh[x/Sqrt[2]])/(x^2-2), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 19 2012 *)
PROG
(Haskell)
a166474 n = a166474_list !! (n-1)
a166474_list = 1 : 2 : zipWith (+)
(tail a166474_list) (zipWith (*) a166474_list $ drop 2 a000217_list)
-- Reinhard Zumkeller, Feb 27 2012
(Magma)
[n le 2 select n else Self(n-1) + Binomial(n, 2)*Self(n-2): n in [1..41]]; // G. C. Greubel, Aug 02 2024
(SageMath)
@CachedFunction
def A166474(n):
if n<3: return n
[A166474(n) for n in range(1, 41)] # G. C. Greubel, Aug 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Nov 05 2009
EXTENSIONS
More terms from Sean A. Irvine, Jun 16 2011
STATUS
approved