This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385947 #12 Jul 13 2025 11:01:10
%S A385947 1,1,7,166,10029,1321025,341733205,160453080950,128422430092385,
%T A385947 166469443066352440,334968718604910165425,1009644894131844004090200,
%U A385947 4422360688027934597152329025,27423466157672001507611296316100,235350249980804930971638499216115775
%N A385947 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+5,5) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385947 E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..4} binomial(4,k) * x^(k+1)/(k+1)! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
%o A385947 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, binomial(j+5, 5)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385947 Cf. A000272, A156325, A385945, A385946, A385948.
%Y A385947 Cf. A385954.
%K A385947 nonn
%O A385947 0,3
%A A385947 _Seiichi Manyama_, Jul 13 2025