A256710 - OEIS

%I #37 Sep 08 2022 08:46:11

%S 0,1,1,1,3,19,165,1777,22771,338011,5700645,107636233,2248959603,

%T 51510798403,1283272040869,34545323506657,999247837611315,

%U 30907592318937451,1017952050849713253,35566506595102088953,1313924839917077864755,51171935743575832547539

%N a(n) = (2*n-3)*a(n-1) - 2*a(n-2), a(0)=0, a(1)=1.

%H Alois P. Heinz, <a href="/A256710/b256710.txt">Table of n, a(n) for n = 0..400</a>

%F E.g.f.: (1/sqrt(2))*sin(sqrt(2)*(1-sqrt(1-2*x))).

%F a(n) ~ cos(sqrt(2)) * 2^(n - 1/2) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Mar 13 2020

%p a:= proc(n) option remember; `if`(n<2, n,

%p       (2*n-3)*a(n-1)-2*a(n-2))

%p     end:

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Apr 10 2015

%t RecurrenceTable[{a[0]==a[1]==1, a[n+2]==(2n+1)a[n+1]-2a[n]}, a, {n, 20}]

%t a[n_]:=(2n-3)*a[n-1]-2a[n-2];a[0]=0;a[1]=1;Array[a,21,0] (* or *)

%t Range[0, 20]! CoefficientList[ Simplify[ Series[ Sin[ Sqrt[2]*(1 - Sqrt[1 - 2 x])]/Sqrt[2], {x, 0, 20}]], x]

%t (* _Robert G. Wilson v_, Apr 08 2015 *)

%t nxt[{n_,a_,b_}]:={n+1,b,b*(2n-1)-2a}; NestList[nxt,{1,0,1},30][[All,2]] (* _Harvey P. Dale_, Jun 21 2020 *)

%o (Magma) [0] cat [n le 2 select 1 else (2*n-3)*Self(n-1)-2*Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Apr 09 2015

%K nonn,easy

%O 0,5

%A _G. C. Greubel_, Apr 08 2015