A398001 - OEIS

%I #9 Jul 17 2026 07:44:16

%S 1,1,3,13,85,781,9399,142729,2668857,60146281,1603662971,49830350261,

%T 1782506062317,72650501193173,3343667983321871,172413153338015185,

%U 9891900891797901745,627629370021134193937,43801226064361529390131,3345934146157974096134941

%N E.g.f. A(x) satisfies A'(x) = 1 + A((exp(2*x) - 1)/2), with A(0) = 0.

%F a(1) = 1; a(n+1) = Sum_{k=1..n} 2^(n-k) * Stirling2(n,k) * a(k).

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

%Y Cf. A003659, A355203, A398002.

%K nonn,new

%O 1,3

%A _Seiichi Manyama_, Jul 17 2026