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

0,5

Links

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

Formula

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

Prog

(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)!));

Crossrefs

Cf. A000248, A216688, A354554.

Sequence in context: A330045 A362349 A274783 * A367719 A293493 A356629

Adjacent sequences: A354550 A354551 A354552 * A354554 A354555 A354556

Keyword

nonn

Author

Seiichi Manyama, Aug 18 2022

Status

approved