A394030 - OEIS

%I #6 Mar 07 2026 11:03:44

%S 1,1,6,48,496,6240,91776,1537088,28798464,595955520,13491708800,

%T 331623830208,8795579682048,250414554029120,7618664812010112,

%U 246723028123216320,8474819292528368640,307805848056790016832,11787380650768137830784,474716135626387606640832,20058947200327244710705920

%N a(0) = 1; a(n) = n * Sum_{j=0..n-1} Sum_{i=0..j} a(i) * a(j-i).

%F G.f. A(x) satisfies: A(x) = 1 + x * d/dx ( x * A(x)^2 / (1 - x) ).

%F a(n) ~ c * n * 2^n * n!, where c = 0.41609792938291784112194732217310... - _Vaclav Kotesovec_, Mar 07 2026

%t a[0] = 1; a[n_] := a[n] = n Sum[Sum[a[i] a[j - i], {i, 0, j}], {j, 0, n - 1}]; Table[a[n], {n, 0, 20}]

%t nmax = 20; A[_] = 0; Do[A[x_] = 1 + x D[x A[x]^2/(1 - x), x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%Y Cf. A000699, A002212, A086871.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 07 2026