cp's OEIS Frontend

A385979 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+2,2) * binomial(n-1,k) * a(k) * a(n-1-k).

%I A385979 #10 Jul 14 2025 10:02:58
%S A385979 1,1,7,145,6449,522096,69506737,14186121706,4212887224905,
%T A385979 1747635451186240,979909591959562571,722787600597422326704,
%U A385979 685585597413868516073953,820283211774547803576454720,1217648676024408903145299884925,2210504358495882876855897821031376
%N A385979 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * binomial(k+2,2) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385979 E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..2} binomial(2,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
%o A385979 (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+2, 2)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385979 Cf. A000272, A156326, A385980, A385981, A385982.
%K A385979 nonn
%O A385979 0,3
%A A385979 _Seiichi Manyama_, Jul 14 2025