A385845 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^4*A'''(x))).
1, 1, 1, 1, 7, 175, 10675, 1291675, 272543461, 91847148373, 46382810082589, 33442006088446669, 33141028037446336195, 43779298038683546954491, 75169054733013247990186039, 164244384592052866115015051119, 448551414321306169623754824645385
Offset: 0
Keywords
Programs
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Mathematica
terms = 17; A[] = 0; Do[A[x] = 1/((1 - x) * (1 - x^4*A'''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 10 2025 *)
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, sum(k=1, 3, stirling(3, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Formula
a(n) = 1 + Sum_{k=0..n-1} (2*k - 3*k^2 + k^3) * a(k) * a(n-1-k).