A362247 Expansion of e.g.f. exp(x * exp(x * (exp(x) - 1))).

1, 1, 1, 7, 37, 201, 1531, 12433, 112729, 1158769, 12920311, 157007841, 2063354437, 29052921769, 436908104179, 6981843029281, 118083965782321, 2106973566128865, 39538081855597807, 778216030845226561, 16027517577057849181, 344635879922587951321

Offset: 0

Author

Seiichi Manyama, Apr 12 2023

Keywords

• nonn

Crossrefs

Cf. A362244, A362245, A362246.

Cf. A000258, A202152.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(x*(exp(x)-1)))))

Formula

a(n) = n! * Sum_{i=0..n} ( Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)! )/i!.