A398001 E.g.f. A(x) satisfies A'(x) = 1 + A((exp(2*x) - 1)/2), with A(0) = 0.

1, 1, 3, 13, 85, 781, 9399, 142729, 2668857, 60146281, 1603662971, 49830350261, 1782506062317, 72650501193173, 3343667983321871, 172413153338015185, 9891900891797901745, 627629370021134193937, 43801226064361529390131, 3345934146157974096134941

Offset

1,3

Links

Table of n, a(n) for n=1..20.

Formula

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

Prog

(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;

Crossrefs

Cf. A003659, A355203, A398002.

Sequence in context: A349582 A246387 A023037 * A354436 A157451 A188204

Adjacent sequences: A397998 A397999 A398000 * A398002 A398006 A398008

Keyword

nonn,new

Author

Seiichi Manyama, Jul 17 2026

Status

approved