A351935 Expansion of e.g.f. exp(x / (1 - x^4/24)).

1, 1, 1, 1, 1, 6, 31, 106, 281, 1261, 10711, 71611, 350461, 1808236, 17037021, 170285116, 1293714241, 8653175441, 84433291741, 1063629264781, 11218379358721, 97926941650546, 1021280770603171, 14623420493573046, 197153396050112041, 2190425085571083901

Offset: 0

Author

Seiichi Manyama, Feb 26 2022

Keywords

• nonn

Crossrefs

Cf. A000262, A351933, A351934, A351936.

Cf. A275423.

Programs

Mathematica

m = 25; Range[0, m]! * CoefficientList[Series[Exp[x/(1 - x^4/24)], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x^4/24))))

PARI

a(n) = if(n<5, 1, sum(k=0, (n-1)\4, (4*k+1)!/24^k*binomial(n-1, 4*k)*a(n-1-4*k)));

Formula

a(n) = Sum_{k=0..floor((n-1)/4)} (4*k+1)!/24^k * binomial(n-1,4*k) * a(n-1-4*k) for n > 4.

a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k)/(24^k * (n-4*k)!). - Seiichi Manyama, Jun 08 2024