A367756 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3) * A(x^4/24)).

1, 1, 3, 13, 73, 386, 2671, 20728, 175393, 1553968, 15520861, 165541806, 1869485773, 22249874518, 284029764383, 3804116563276, 53328350650081, 782331158754088, 12051288543702313, 193028133988081918, 3212490296905001781, 55543932173668760221

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/4)) * a(n-1-k) / (24^floor(k/4) * floor(k/4)! * (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\4+1]*v[i-j]/(24^(j\4)*(j\4)!*(i-1-j)!))); v;

Crossrefs

Cf. A367754, A367755, A367757.

Cf. A143568.

Sequence in context: A090754 A067764 A193930 * A063512 A199317 A205776

Adjacent sequences: A367753 A367754 A367755 * A367757 A367758 A367759

Keyword

nonn

Author

Seiichi Manyama, Nov 29 2023

Status

approved