A385846 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^5*A''''(x))).
1, 1, 1, 1, 1, 25, 3025, 1092025, 918393025, 1543818675025, 4670051491951201, 23541729570926148241, 186474039931306081488961, 2215498068423847604734793641, 38020162352221648825602734209201, 913434400512125113270449340963296649, 29925024395177730837015182640209851847809
Offset: 0
Keywords
Programs
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Mathematica
terms = 17; A[] = 0; Do[A[x] = 1/((1 - x) * (1 - x^5*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, 4, stirling(4, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Formula
a(n) = 1 + Sum_{k=0..n-1} (-6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).