A386211 G.f. A(x) satisfies A(x) = 1/(1-x)^2 + x^2*A(x)*A'(x).

1, 2, 5, 18, 89, 556, 4127, 35084, 334049, 3510574, 40300769, 501455462, 6721438253, 96561557816, 1480441163151, 24132225315816, 416852189961737, 7607668036964506, 146296367990498941, 2957053490913146762, 62682940163232269033, 1390605993609167492932

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..446

Formula

a(n) = n + 1 + (n-1)/2 * Sum_{k=0..n-1} a(k) * a(n-1-k).

a(n) = n + 1 + Sum_{k=0..n-1} k * a(k) * a(n-1-k).

a(n) ~ c * n! * n, where c = 1.4406730618690233665395265348... - Vaclav Kotesovec, Aug 05 2025

Mathematica

terms = 22; A[_] = 1; Do[A[x_] = 1/(1-x)^2+x^2*A[x]A'[x] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 16 2025 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+(i-1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143917, A386212.

Cf. A386209.

Sequence in context: A005500 A020025 A113715 * A227094 A173227 A099556

Adjacent sequences: A386208 A386209 A386210 * A386212 A386213 A386214

Keyword

nonn

Author

Seiichi Manyama, Jul 15 2025

Status

approved