A386238 G.f. A(x) satisfies A(x) = 1/( (1+x) * (1 - x*A(x) - x^2*A'(x)) ).

1, 0, 1, 3, 16, 98, 708, 5827, 53758, 548879, 6142379, 74756975, 983186673, 13897204929, 210128473576, 3384688592135, 57868599692392, 1046744442623159, 19972732558110246, 400941834927714249, 8447457715944191407, 186387757159393453454, 4298157267300757437962

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

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

Mathematica

terms = 23; A[_] = 1; Do[A[x_] = 1/((1+x)(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]=(-1)^i+(i+1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;

Crossrefs

Cf. A321087, A386239.

Sequence in context: A295810 A233203 A074553 * A303831 A193037 A363573

Adjacent sequences: A386235 A386236 A386237 * A386239 A386240 A386241

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2025

Status

approved