%I #11 Dec 04 2023 06:12:52

%S 1,-1,3,-4,25,24,721,5942,82209,1186280,19956241,373942194,7768988833,

%T 177018731876,4389959146665,117700102748654,3392361669670081,

%U 104592876707106672,3434908281762030049,119702402508549928490,4411764405039931048641

%N Expansion of e.g.f. exp(-x * sqrt(1-2*x)).

%F a(n) = (-1)^n * n! * Sum_{k=0..n} 2^k * binomial((n-k)/2,k)/(n-k)!.

%F D-finite with recurrence a(n) +2*(-n+3)*a(n-1) +2*(-3*n+10)*a(n-2) +6*(n-2)*a(n-3) -9*(n-3)^2*a(n-4) -27*(n-3)*(n-4)*a(n-5)=0. - _R. J. Mathar_, Dec 04 2023

%p A362165 := proc(n)

%p (-1)^n*n!*add(2^k * binomial((n-k)/2,k)/(n-k)!,k=0..n) ;

%p end proc:

%p seq(A362165(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*sqrt(1-2*x))))

%Y Cf. A115329, A362161, A362163.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 10 2023