A351970 - OEIS

%I #9 May 30 2022 09:53:43

%S 1,1,1,2,5,11,22,43,85,171,351,738,1590,3498,7827,17757,40725,94113,

%T 218439,507852,1180395,2739312,6342084,14642100,33703182,77344686,

%U 176984406,403901722,919533655,2089000936,4737194867,10726221713,24257223605,54805216567

%N a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} binomial(n,3*k) * a(k).

%H Seiichi Manyama, <a href="/A351970/b351970.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f. A(x) satisfies: A(x) = A(x^3/(1 - x)^3) / (1 - x).

%F E.g.f.: exp(x) * Sum_{n>=0} a(n) * x^(3*n) / (3*n)!.

%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k] a[k], {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 33}]

%t nmax = 33; A[_] = 1; Do[A[x_] = A[x^3/(1 - x)^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%Y Cf. A027826, A351971.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Feb 26 2022