A394030 a(0) = 1; a(n) = n * Sum_{j=0..n-1} Sum_{i=0..j} a(i) * a(j-i).

1, 1, 6, 48, 496, 6240, 91776, 1537088, 28798464, 595955520, 13491708800, 331623830208, 8795579682048, 250414554029120, 7618664812010112, 246723028123216320, 8474819292528368640, 307805848056790016832, 11787380650768137830784, 474716135626387606640832, 20058947200327244710705920

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

a(n) ~ c * n * 2^n * n!, where c = 0.41609792938291784112194732217310... - Vaclav Kotesovec, Mar 07 2026

Mathematica

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}]
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]

Crossrefs

Cf. A000699, A002212, A086871.

Sequence in context: A051578 A052639 A248744 * A261900 A055861 A053506

Adjacent sequences: A394027 A394028 A394029 * A394031 A394033 A394034

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 07 2026

Status

approved