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

%I

%S 1,4,16,74,402,2542,18446,151482,1390738,14126582,157365222,

%T 1908110866,25022451482,352918443438,5327630246542,85716034274282,

%U 1464281837606946,26470821156031462,504879319309407158,10132393298394712002,213441590598213760042

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

%H Alois P. Heinz, <a href="/A306495/b306495.txt">Table of n, a(n) for n = 0..448</a>

%F a(n) = Sum_{k=-n..n} A324224(n+1,k).

%F 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 egf:= (2-exp(-x))*exp(x)/(x-1)^2:

%p a:= n-> n! * coeff(series(egf, x, n+1), x, n):

%p seq(a(n), n=0..23);

%p # second Maple program:

%p a:= proc(n) option remember; `if`(n<3, 4^n,

%p (2*n+1)*a(n-1)-(n+2)*(n-1)*a(n-2)+(n-1)*(n-2)*a(n-3))

%p end:

%p seq(a(n), n=0..23);

%Y Row sums of A324224(n+1).

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 19 2019

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Last modified February 9 07:25 EST 2023. Contains 360153 sequences. (Running on oeis4.)