A386265 G.f. A(x) satisfies A(x) = 1/(1+x) + x^2 * (d/dx A(x)^2).

1, -1, -1, -3, -11, -61, -469, -4711, -58071, -842361, -13995017, -261468651, -5420285859, -123390215413, -3058937910365, -82014781572431, -2364353822942639, -72922308541928945, -2395804482405465233, -83528123730918481747, -3079941980238262567995

Offset

0,4

Links

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

Formula

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

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

Mathematica

terms=21; A[_]=1; Do[A[x_]=1/(1+x) + 2x^2 * A[x]A'[x] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 17 2025 *)

Prog

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

Crossrefs

Cf. A386208, A386239, A386266.

Sequence in context: A395377 A024528 A368880 * A273468 A004108 A203007

Adjacent sequences: A386262 A386263 A386264 * A386266 A386267 A386268

Keyword

sign

Author

Seiichi Manyama, Jul 17 2025

Status

approved