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%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
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