A385839 - OEIS

%I #11 Jul 10 2025 11:00:15

%S 1,2,7,471,345240,1415486250,22122636527386,1032242227753172079,

%T 121446394933841583123508,31836929544298684420302348229,

%U 16919577022277987344334514604394117,16919644700745370569015746375165719379327,29974250364360598877961318618919670090162246645

%N a(n) = 1 + Sum_{k=0..n-1} (1 + k^6) * a(k) * a(n-1-k).

%F G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*A(x) - x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ) ).

%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+j^6)*v[j+1]*v[i-j])); v;

%Y Cf. A321087, A385835, A385836, A385837, A385838.

%Y Cf. A385834.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 09 2025