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%I #10 Dec 18 2017 04:14:59
%S 0,1,5,22,100,493,2701,16678,116704,923473,8204077,81069166,882762292,
%T 10503611245,135576241957,1886597854894,28151936397856,
%U 448397396131969,7592570340752053,136187683731334054,2579494839314653540,51445637954467827661
%N a(n) = e^3 * Sum_{k=0..n-1} Gamma(k + 1, 3).
%F a(n) = (3*n-6)*a(n-3)+(4-4*n)*a(n-2)+(3+n)*a(n-1) for n >= 3.
%F E.g.f.: exp(x+2)*(Ei(1,2-2*x)-Ei(1,2)). - _Robert Israel_, Dec 17 2017
%p a := proc(n) option remember; if n=0 then 0 elif n=1 then 1 elif n=2 then 5 else
%p (3*n-6)*a(n-3)+(4-4*n)*a(n-2)+(3+n)*a(n-1) fi end: seq(a(n), n=0..21);
%t a[n_] := E^3 Sum[Gamma[k + 1, 3], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]
%o (PARI) a=vector(1000); a[1]=1;a[2]=5;a[3]=22;for(n=4, #a, a[n] = (n+3)*a[n-1]+(4-4*n)*a[n-2]+(3*n-6)*a[n-3]); va=concat(0, vector(1000, n, a[n])) \\ _Altug Alkan_, Dec 17 2017
%Y Cf A053486, A295518.
%K nonn
%O 0,3
%A _Peter Luschny_, Dec 17 2017
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