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%I #13 Jan 30 2024 08:23:44
%S 1,3,15,117,1305,19323,359559,8084205,213425361,6475518675,
%T 222088463199,8497641269637,358899729493545,16585866328129803,
%U 832523413971932055,45105537151437499197,2623613865509122341921,163070009495928522691875
%N Expansion of e.g.f. exp( (3/2) * (1-sqrt(1-4*x)) ).
%F a(0) = 1; a(n) = Sum_{k=0..n-1} 3^(n-k) * (n-1+k)! / (k! * (n-1-k)!).
%F a(n) = 2*(2*n-3)*a(n-1) + 9*a(n-2).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3/2*(1-sqrt(1-4*x)))))
%Y Cf. A001517, A101682, A243953, A369723, A369724.
%Y Cf. A000108.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 30 2024
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