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 A386506 #10 Jul 24 2025 07:23:10
%S A386506 1,1,3,79,8845,2875301,2173904341,3302241027205,9087841330660905,
%T A386506 41958697476222137161,306298931820000949752841,
%U A386506 3372659958223293180648888761,53908617652925799897200239787869,1211704268213547361986251511514073293,37286568732242131447316119558759880633085
%N A386506 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^3 * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386506 E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ).
%o A386506 (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)*j^3*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386506 Cf. A143925, A386505, A386507, A386508, A386509.
%Y A386506 Cf. A385940, A386444.
%K A386506 nonn
%O A386506 0,3
%A A386506 _Seiichi Manyama_, Jul 24 2025