A386208 G.f. A(x) satisfies A(x) = 1/(1-x) + x^2 * (d/dx A(x)^2).

1, 1, 3, 15, 109, 1029, 11831, 159595, 2466073, 42920585, 830791243, 17706459431, 412116616517, 10403094478669, 283137307529727, 8266131486719107, 257710382446835761, 8546074646120275473, 300384437888406796051, 11155675460369469443263, 436506923733804200244509

Offset: 0

Author

Seiichi Manyama, Jul 15 2025

Keywords

• nonn

Crossrefs

Cf. A386209, A386210.

Cf. A143917, A185183, A376125.

Programs

PARI

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

Formula

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

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