A361558 Expansion of e.g.f. exp((x + x^2/2 + x^3/6 + x^4/24)/(1-x)).

1, 1, 4, 20, 127, 976, 8776, 90084, 1037555, 13233077, 184956386, 2809098986, 46038214729, 809411443790, 15189361799522, 302932433571356, 6396529241755881, 142523960797017589, 3341115707515530400, 82187749261419720712, 2116421112495023612311

Offset: 0

Author

Seiichi Manyama, Mar 15 2023

Keywords

• nonn

Crossrefs

Cf. A361532, A361548, A361557.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x+x^2/2+x^3/6+x^4/24)/(1-x))))

Formula

a(n) = (2*n-1) * a(n-1) - (n-1)*(n-3) * a(n-2) - binomial(n-1,3) * a(n-4) - 3*binomial(n-1,4) * a(n-5) for n > 4.