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 A385945 #8 Jul 13 2025 11:01:18
%S A385945 1,1,5,63,1533,62736,3969387,366744330,47441881377,8313978813120,
%T A385945 1921417594566561,572533956456137424,215766174031503450885,
%U A385945 101144655173329674617088,58127411808811103704523775,40435528907318329027426583376,33666103690446265067517343384833
%N A385945 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+3,3) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385945 E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..2} binomial(2,k) * x^(k+1)/(k+1)! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
%o A385945 (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+3, 3)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385945 Cf. A000272, A156325, A385946, A385947, A385948.
%Y A385945 Cf. A385952.
%K A385945 nonn
%O A385945 0,3
%A A385945 _Seiichi Manyama_, Jul 13 2025