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