A386229 G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - x^2*A'(x)) ).

1, 3, 12, 70, 535, 4908, 51478, 600584, 7662285, 105684465, 1563183259, 24645719004, 412279514088, 7290426692472, 135862518564330, 2661378323466016, 54675576786754501, 1175673956931922257, 26411686616265112230, 618863341216409971750, 15101129008183181824938

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

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

Mathematica

terms = 21; A[_] = 1; Do[A[x_] = 1/((1-x)^2(1-x*A[x]-x^2*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)*(1+sum(j=0, i-1, v[j+1]*v[i-j])/2)); v;

Crossrefs

Cf. A088716, A321087, A386230.

Cf. A386211.

Sequence in context: A001205 A346888 A330493 * A112320 A103366 A335643

Adjacent sequences: A386226 A386227 A386228 * A386230 A386231 A386232

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2025

Status

approved