A367748 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2) * A(x^3)).

1, 1, 3, 13, 73, 501, 4051, 40153, 434673, 5231593, 71641891, 1051099941, 16673401273, 289579557853, 5336892479283, 104679769486321, 2199654959898721, 48682858073000913, 1135029742772833603, 27968526823231736893, 721419709386600131241

Offset: 0

Author

Seiichi Manyama, Nov 29 2023

Keywords

• nonn

Crossrefs

Cf. A367747, A367749, A367751.

Cf. A367652, A367719.

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\3+1]*v[i-j]/((j\3)!*(i-1-j)!))); v;

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/3)) * a(n-1-k) / (floor(k/3)! * (n-1-k)!).