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Expansion of e.g.f. exp(2*x + x^2 * exp(x)).
1

%I #10 Aug 23 2024 02:11:54

%S 1,2,6,26,136,812,5494,41414,341800,3056984,29415274,302501498,

%T 3305797444,38212967444,465409979038,5951991056558,79686155008816,

%U 1113909729606896,16219814971477330,245503998889083362,3855373914424695196,62708526467241370892

%N Expansion of e.g.f. exp(2*x + x^2 * exp(x)).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (k+2)^(n-2*k) / (k! * (n-2*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x+x^2*exp(x))))

%o (PARI) a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(k!*(n-2*k)!));

%Y Cf. A216507, A375651.

%Y Cf. A367874, A375629.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 22 2024