A385764 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^5*A''''(x)).
1, 1, 2, 5, 14, 378, 46500, 16879869, 14229776750, 23948731244678, 72492823741526156, 365581334105823084634, 2896500982661242290253612, 34419121542689992919239814260, 590735385934420874267059790772360, 14193599152271246770955912922939691797, 465024889616667096875210999651863472880846
Offset: 0
Keywords
Programs
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Mathematica
terms = 17; A[] = 0; Do[A[x] = 1/(1-x*A[x]-x^5*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, 4, stirling(4, k, 1)*j^k))*v[j+1]*v[i-j])); v;
Formula
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 - 6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).