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 A386513 #9 Jul 24 2025 07:25:07
%S A386513 1,1,3,61,5365,1529521,1165598707,2064316175293,7646264783133257,
%T A386513 54571471797846058921,702880914451594090404601,
%U A386513 15486578255494092846454504205,558260219954065540499622238580509,31707506930744375037184483066962163261,2747328696602823034266635550466257234352117
%N A386513 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+4,5) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386513 E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..5} binomial(4,k-1) * x^k/k! * (d^k/dx^k A(x)) ).
%o A386513 (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)*binomial(j+4, 5)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386513 Cf. A143925, A386510, A386511, A386512.
%Y A386513 Cf. A385947, A386455.
%K A386513 nonn
%O A386513 0,3
%A A386513 _Seiichi Manyama_, Jul 24 2025