A386453 - OEIS

%I #8 Jul 22 2025 09:51:36

%S 1,1,2,11,131,2888,107027,6212005,534389458,65203760863,

%T 10889677250198,2417582805875622,696275799766601842,

%U 254839529849806176727,116462397939843834894367,65452132793842930368844779,44638474752168615525812508053,36514339485766910607857620043816

%N a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} binomial(k+2,3) * a(k) * a(n-1-k).

%F G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..3} binomial(2,k-1) * x^k/k! * (d^k/dx^k A(x)) ).

%o (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, binomial(j+2, 3)*v[j+1]*v[i-j])); v;

%Y Cf. A075834, A386452, A386454, A386455.

%Y Cf. A385875.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 22 2025