A354553 Expansion of e.g.f. exp( x * exp(x^3) ).

1, 1, 1, 1, 25, 121, 361, 3361, 42001, 275185, 1819441, 30777121, 371238121, 3057311401, 44263763545, 801096528961, 9710981323681, 125367419194081, 2643123767954401, 45840730383002305, 646414025466298681, 13258301279836276441

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..475

Crossrefs

Cf. A000248, A216688, A354554.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3)))))

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(k!*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(k! * (n - 3*k)!).