A385876 a(n) = 1 + Sum_{k=0..n-1} binomial(k+3,4) * a(k) * a(n-1-k).
1, 1, 2, 12, 193, 6968, 495189, 62906143, 13274340034, 4393943557987, 2179423896462618, 1560476564415661780, 1563601961040080858376, 2135883440687340361131857, 3889446901597262416621276499, 9260777373178278371280728311304, 28347247357191779349093896687278933
Offset: 0
Keywords
Programs
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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, binomial(j+3, 4)*v[j+1]*v[i-j])); v;
Formula
G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..4} binomial(3,k-1) * x^k/k! * (d^k/dx^k A(x)) ) ).