OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x)^2.
E.g.f.: 1 + exp(x) * Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)!.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 32}]
nmax = 32; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 07 2022
STATUS
approved