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A306495 Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2.

%I A306495 #9 Feb 19 2019 18:50:53
%S A306495 1,4,16,74,402,2542,18446,151482,1390738,14126582,157365222,
%T A306495 1908110866,25022451482,352918443438,5327630246542,85716034274282,
%U A306495 1464281837606946,26470821156031462,504879319309407158,10132393298394712002,213441590598213760042
%N A306495 Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2.
%H A306495 Alois P. Heinz, <a href="/A306495/b306495.txt">Table of n, a(n) for n = 0..448</a>
%F A306495 a(n) = Sum_{k=-n..n} A324224(n+1,k).
%F A306495 a(n) = (2*n+1)*a(n-1) - (n+2)*(n-1)*a(n-2) + (n-1)*(n-2)*a(n-3) for n > 2, a(n) = 4^n for n < 3.
%p A306495 egf:= (2-exp(-x))*exp(x)/(x-1)^2:
%p A306495 a:= n-> n! * coeff(series(egf, x, n+1), x, n):
%p A306495 seq(a(n), n=0..23);
%p A306495 # second Maple program:
%p A306495 a:= proc(n) option remember; `if`(n<3, 4^n,
%p A306495       (2*n+1)*a(n-1)-(n+2)*(n-1)*a(n-2)+(n-1)*(n-2)*a(n-3))
%p A306495     end:
%p A306495 seq(a(n), n=0..23);
%Y A306495 Row sums of A324224(n+1).
%K A306495 nonn
%O A306495 0,2
%A A306495 _Alois P. Heinz_, Feb 19 2019