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A367719
E.g.f. satisfies A(x) = exp(x*A(x^3)).
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.
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. A354553.
Sequence in context: A362349 A274783 A354553 * A293493 A356629 A362571
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 28 2023
STATUS
approved