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E.g.f. A(x) satisfies A(x) = (1 + (exp(x) - 1) * A(3*x)) / (1 - x).
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%I #8 Dec 02 2023 13:14:11

%S 1,2,17,529,60191,24822701,36413854321,186201636968159,

%T 3260017071214457747,192544750449664642891369,

%U 37901471231124512743264725077,24619109083914012570141331273785011,52334858943702505364559907161989713988743

%N E.g.f. A(x) satisfies A(x) = (1 + (exp(x) - 1) * A(3*x)) / (1 - x).

%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 3^(n-k) * 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]+sum(j=1, i, 3^(i-j)*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A006155, A367830.

%Y Cf. A367836.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023