A108204 a(n) = 2*(n-1)*a(n-1) -(n-1)*a(n-2) with a(0)=0, a(1)=1.

0, 1, 2, 6, 30, 216, 2010, 22824, 305466, 4704864, 81938358, 1591718520, 34116485502, 799695029808, 20348556463482, 558563850560184, 16451687169853290, 517516967826342336, 17315898224208133494

Offset

0,3

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 0..404

Formula

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

Maple

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):
map(f, [$0..50]); # Robert Israel, Jun 11 2018

Mathematica

M[n_] := {{0, -1}, {(n - 1), 2*(n - 1)}};
v[1] = {0, 1};
v[n_] := v[n] = M[n].v[n - 1];
a = Table[Abs[v[n][[1]]], {n, 1, 25}]
(* Second program: *)
Nest[Append[#, 2 (Length[#] - 1) Last[#] - (Length[#] - 1) #[[-2]]] &, {0, 1}, 17] (* Michael De Vlieger, Jun 11 2018 *)

Crossrefs

Cf. A000166.

Sequence in context: A161620 A333508 A205569 * A088160 A112317 A089459

Adjacent sequences: A108201 A108202 A108203 * A108205 A108206 A108207

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 15 2005

Extensions

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

Status

approved