A352300 Expansion of e.g.f. 1/(2 - exp(x) - x^4).

1, 1, 3, 13, 99, 781, 7563, 84253, 1103595, 16074589, 260443083, 4630046653, 90017588235, 1894771249021, 42957132108075, 1043136555486493, 27024421701469995, 743851294350730141, 21679544916491784843, 666932347454809048189

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A006155, A346269, A352299.

Cf. A352304.

Programs

Mathematica

m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^4), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^4)))

PARI

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

Formula

a(n) = n * (n-1) * (n-2) * (n-3) * a(n-4) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 3.