A385761 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^6*A'''''(x))).
1, 2, 5, 15, 51, 188, 23291, 16862710, 42561503035, 286183563337662, 4328240254531111671, 130903298544350358627387, 7257802488822060515691899445, 689810579878520205782663179307100, 106537105206016369903910237449838232525, 25594900303804029125790200935921438169789415
Offset: 0
Keywords
Programs
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Mathematica
terms = 16; A[] = 0; Do[A[x] = 1/((1-x)*(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)); for(i=0, n, v[i+1]=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(n) = 1 + 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).