A367755 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2) * A(x^3/6)).

1, 1, 3, 13, 53, 301, 1951, 13203, 105673, 919873, 8472491, 86799241, 948033373, 10924180853, 135880443063, 1780842778471, 24496224075921, 357483642165313, 5454904465819603, 86909842633518373, 1453042115780967941, 25262405474642837341

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/3)) * a(n-1-k) / (6^floor(k/3) * floor(k/3)! * (n-1-k)!).

Prog

(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]/(6^(j\3)*(j\3)!*(i-1-j)!))); v;

Crossrefs

Cf. A367754, A367756, A367757.

Cf. A143567.

Sequence in context: A151209 A151210 A151211 * A121240 A065839 A066611

Adjacent sequences: A367752 A367753 A367754 * A367756 A367757 A367758

Keyword

nonn

Author

Seiichi Manyama, Nov 29 2023

Status

approved