A386511 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+2,3) * binomial(n-1,k) * a(k) * a(n-1-k).
1, 1, 3, 43, 1889, 198661, 42947941, 17142237365, 11658352652969, 12696712215226345, 21077148910182673081, 51239319321668728761281, 176469705716413028667777349, 837352955330191136544190873989, 5345677943448502627987168885274813, 44983970430636919384496638254796550221
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*binomial(j+2, 3)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..3} binomial(2,k-1) * x^k/k! * (d^k/dx^k A(x)) ).