A352308 Expansion of e.g.f. 1/(2 - exp(x) - x^4/24).

1, 1, 3, 13, 76, 551, 4803, 48833, 567465, 7418263, 107752293, 1721642143, 30008756055, 566650322031, 11523037802461, 251062618129063, 5834798259848815, 144078299659541361, 3766993649599221903, 103961442644871088897, 3020133228180079209075

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A006155, A352306, A352307.

Cf. A352300.

Programs

Mathematica

m = 20; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^4/24), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^4/24)))

PARI

b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m))*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 4);

Formula

a(n) = binomial(n,4) * a(n-4) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 3.