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 A385981 #8 Jul 14 2025 10:02:48
%S A385981 1,1,11,526,75981,27017601,20599793857,30432196412318,
%T A385981 80590529100023889,359767027014797719000,2575966649397129017224661,
%U A385981 28392489655027195386265889544,465411261102140455922541427819489,11017701081052339904298545720453122836,367264434033142995461894471693185212854475
%N A385981 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+4,4) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385981 E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..4} binomial(4,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
%o A385981 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j+1)*binomial(j+4, 4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385981 Cf. A000272, A156326, A385979, A385980, A385982.
%K A385981 nonn
%O A385981 0,3
%A A385981 _Seiichi Manyama_, Jul 14 2025