A351936 Expansion of e.g.f. exp(x / (1 - x^5/5!)).

1, 1, 1, 1, 1, 1, 7, 43, 169, 505, 1261, 5545, 55441, 442729, 2540539, 11381371, 54534481, 548974609, 6572212921, 59711454433, 413207026561, 2551872368305, 24405087826351, 356232375255835, 4526838244526137, 44179554690486601, 358234717042702501

Offset: 0

Author

Seiichi Manyama, Feb 26 2022

Keywords

• nonn

Crossrefs

Cf. A000262, A351933, A351934, A351935.

Programs

Mathematica

m = 26; Range[0, m]! * CoefficientList[Series[Exp[x/(1 - x^5/5!)], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x^5/5!))))

PARI

a(n) = if(n<6, 1, sum(k=0, (n-1)\5, (5*k+1)!/5!^k*binomial(n-1, 5*k)*a(n-1-5*k)));

Formula

a(n) = Sum_{k=0..floor((n-1)/5)} (5*k+1)!/(5!)^k * binomial(n-1,5*k) * a(n-1-5*k) for n > 5.

a(n) = n! * Sum_{k=0..floor(n/5)} binomial(n-4*k-1,k)/(120^k * (n-5*k)!). - Seiichi Manyama, Jun 08 2024