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 A385980 #9 Jul 14 2025 10:02:55
%S A385980 1,1,9,295,24921,4504516,1543745107,919392117722,890353538984905,
%T A385980 1330464112593541120,2940642877993896450701,9284167814032856189142864,
%U A385980 40666099850492306669400356041,241073945237343019120798232332320,1893421587381601800604423881821405775
%N A385980 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+3,3) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385980 E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..3} binomial(3,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
%o A385980 (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+3, 3)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385980 Cf. A000272, A156326, A385979, A385981, A385982.
%Y A385980 Cf. A385946, A385952.
%K A385980 nonn
%O A385980 0,3
%A A385980 _Seiichi Manyama_, Jul 14 2025