A385765 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^6*A'''''(x)).
1, 1, 2, 5, 14, 42, 5172, 3739389, 9434483630, 63428037194102, 959222215928392076, 29009757539769286481866, 1608387988236777669667251772, 152866019594999736359695792369300, 23609086665918990295149462904374925800, 5671917808033245221993631555503554148332485
Offset: 0
Keywords
Programs
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Mathematica
terms = 16; A[] = 0; Do[A[x] = 1/(1-x*A[x]-x^6*A'''''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 2025 *)
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+sum(k=1, 5, stirling(5, k, 1)*j^k))*v[j+1]*v[i-j])); v;
Formula
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + 24*k - 50*k^2 + 35*k^3 - 10*k^4 + k^5) * a(k) * a(n-1-k).