A367719 E.g.f. satisfies A(x) = exp(x*A(x^3)).

1, 1, 1, 1, 25, 121, 361, 3361, 42001, 275185, 1819441, 30777121, 371238121, 9284332201, 131442054745, 1454933712961, 34120902859681, 851562584890081, 12300037440760801, 187928965721651905, 6019555345508794681, 130768735411230580441

Offset

0,5

Comments

This sequence is different from A354553.

Links

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/3)} (3*k+1) * a(k) * a(n-1-3*k) / (k! * (n-1-3*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)\3, (3*j+1)*v[j+1]*v[i-3*j]/(j!*(i-1-3*j)!))); v;

Crossrefs

Cf. A138292, A367720.

Cf. A354553.

Sequence in context: A362349 A274783 A354553 * A293493 A356629 A362571

Adjacent sequences: A367716 A367717 A367718 * A367720 A367721 A367722

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2023

Status

approved