A396965 E.g.f. A(x) satisfies A(x) = 1 + x * A(x * exp(2*x)).

1, 1, 2, 18, 216, 4360, 125040, 4757424, 233179520, 14258991744, 1060121721600, 94009965280000, 9789344262601728, 1181209592291349504, 163306868988824078336, 25621879112031299758080, 4524060645635205169643520, 892453349895680565864595456, 195425578879660458241000538112

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} (2*k)^(n-k-1) * binomial(n-1,k) * a(k).

a(0) = 1; a(n) = n * A397882(n-1).

E.g.f.: 1 + x*B(x), where B(x) is the e.g.f. of A397882.

Example

A(x)         = 1 + x + x^2 + 3*x^3 + 9*x^4 + 109/3*x^5 + 521/3*x^6 + ...
A(x * exp(2*x)) =  1 + x   + 3*x^2 + 9*x^3 + 109/3*x^4 + 521/3*x^5 + ...

Prog

(PARI) a_vector(n, s=2, t=0) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(k=0, i-1, (s*k+t)^(i-k-1)*binomial(i-1, k)*v[k+1])); v;

Crossrefs

Cf. A000142, A395666.

Cf. A397881, A397882.

Cf. A397858.

Sequence in context: A052726 A217239 A279045 * A155666 A355723 A384521

Adjacent sequences: A396962 A396963 A396964 * A396966 A396967 A396968

Keyword

nonn,new

Author

Seiichi Manyama, Jul 13 2026

Status

approved