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Expansion of e.g.f. 1/(3 - x - 2*exp(x)).
1

%I #13 Dec 05 2023 09:01:38

%S 1,3,20,200,2666,44422,888214,20719722,552385386,16567346630,

%T 552104425070,20238679934002,809341290336274,35062535546332062,

%U 1635835480858764342,81770970437144725034,4360009179878123161658,247004345719314584973430

%N Expansion of e.g.f. 1/(3 - x - 2*exp(x)).

%F a(0) = 1; a(n) = n * a(n-1) + 2 * Sum_{k=1..n} binomial(n,k) * a(n-k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+2*sum(j=1, i, binomial(i, j)*v[i-j+1])); v;

%Y Cf. A006155, A367925.

%Y Cf. A004123, A367830, A367835, A367922.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 05 2023