A376086 a(0) = 1; a(n) = Sum_{k=0..n-1} (3*k+2) * a(k) * a(n-k-1).

1, 2, 14, 160, 2444, 45792, 1005480, 25169760, 705321200, 21841420384, 740194188032, 27243674154368, 1082259310732096, 46159435144505600, 2104195645965319680, 102113572703197079040, 5256795948307255075584, 286171738279517073904128, 16427146596936396844976640

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

G.f. A(x) satisfies: A(x) = 1 + 2 * x * A(x)^2 + 3 * x^2 * A'(x) * A(x).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(3 k + 2) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[_] = 0; Do[A[x_] = 1 + 2 x A[x]^2 + 3 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000699, A005159, A088716, A215648, A375393, A376087.

Sequence in context: A354242 A268011 A052112 * A354241 A364398 A074635

Adjacent sequences: A376083 A376084 A376085 * A376087 A376088 A376089

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 09 2024

Status

approved