A166474 a(1)=1; a(2)=2; for n>2, a(n)=a(n-1)+A000217(n-1)*a(n-2).

1, 2, 5, 17, 67, 322, 1729, 10745, 72989, 556514, 4570909, 41300833, 397831735, 4156207538, 45928539713, 544673444273, 6790954845241, 90125991819010, 1251379270355221, 18375317715967121, 281164964490563531, 4525863356878968482

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

a(n+1) = A166469(A066120(n)).

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

Crossrefs

Cf. A166469, A066120, A351046.

Sequence in context: A062881 A122206 A104082 * A054769 A003510 A051625

Adjacent sequences: A166471 A166472 A166473 * A166475 A166476 A166477

Keyword

nonn

Author

Matthew Vandermast, Nov 05 2009

Extensions

More terms from Sean A. Irvine, Jun 16 2011

Status

approved