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
Keywords
Programs
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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 *)
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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;
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).