A354552 Expansion of e.g.f. exp( x * exp(x^4/24) ).

1, 1, 1, 1, 1, 6, 31, 106, 281, 946, 7561, 54286, 281161, 1207636, 7997991, 81996916, 701522641, 4580581916, 29742355441, 306369616636, 3632198902321, 34710574441096, 276645112305871, 2652825718776696, 35647605796451881, 458142859493786776

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Comments

This sequence is different from A143568.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..533

Crossrefs

Cf. A000248, A354550, A354551.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^4/24)))))

PARI

a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(24^k*k!*(n-4*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(24^k * k! * (n - 4*k)!).