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

%I #8 Dec 07 2023 08:27:15

%S 1,3,14,89,727,7322,88067,1233815,19745180,355434387,7108803715,

%T 156394360300,3753468860797,97590218025159,2732526295603774,

%U 81975790251071765,2623225298514438627,89189660232355783122

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

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

%F a(n) = n! * Sum_{k=0..n} 2^(n-k) * Bell(k)/k!, where Bell() is A000110.

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

%Y Cf. A000110, A367972.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Dec 06 2023