A367749 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3) * A(x^4)).

1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4777993, 62569891, 893927541, 13827333433, 234241234813, 4212828738483, 80727388033321, 1641227208417121, 35581993575319953, 810641581182744643, 19416795485684156893, 487647253209539939241

Offset: 0

Author

Seiichi Manyama, Nov 29 2023

Keywords

• nonn

Crossrefs

Cf. A367747, A367748, A367751.

Cf. A367653, A367720.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=0, i-1, (j+1)*v[j\4+1]*v[i-j]/((j\4)!*(i-1-j)!))); v;

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/4)) * a(n-1-k) / (floor(k/4)! * (n-1-k)!).