A108204 - OEIS

%I #10 Jun 12 2018 02:43:30

%S 0,1,2,6,30,216,2010,22824,305466,4704864,81938358,1591718520,

%T 34116485502,799695029808,20348556463482,558563850560184,

%U 16451687169853290,517516967826342336,17315898224208133494

%N a(n) = 2*(n-1)*a(n-1) -(n-1)*a(n-2) with a(0)=0, a(1)=1.

%C This is also the (2,2) element of the product matrix after multiplying the unit matrix from the left by the matrices (0,-1;j-1,2j-2) in the order j=2 to n.

%H Robert Israel, <a href="/A108204/b108204.txt">Table of n, a(n) for n = 0..404</a>

%F E.g.f.: exp(x/2) (1-2x)^(1/4) Int_{0..x} exp(-t/2) (1-2t)^(-5/4) dt satisfies the d.e. (1-2x) y' + x y = 1, y(0)=0. - _Robert Israel_, Jun 11 2018

%p f:= gfun:-rectoproc({a(n)=2*(n-1)*a(n-1) -(n-1)*a(n-2),a(0)=0,a(1)=1},a(n),remember):

%p map(f, [$0..50]); # _Robert Israel_, Jun 11 2018

%t M[n_] := {{0, -1}, {(n - 1), 2*(n - 1)}};

%t v[1] = {0, 1};

%t v[n_] := v[n] = M[n].v[n - 1];

%t a = Table[Abs[v[n][[1]]], {n, 1, 25}]

%t (* Second program: *)

%t Nest[Append[#, 2 (Length[#] - 1) Last[#] - (Length[#] - 1) #[[-2]]] &, {0, 1}, 17] (* _Michael De Vlieger_, Jun 11 2018 *)

%Y Cf. A000166.

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Jun 15 2005

%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009