A373517 - OEIS

%I #14 Jun 10 2024 10:02:28

%S 1,1,1,1,9,41,121,1401,11761,61489,864081,10597841,81833401,

%T 1350154521,21715461769,225232218121,4267472824161,84597818284001,

%U 1111699778741281,23801969674626849,558853937533757161,8943028907965939081,213696639293901810201

%N Expansion of e.g.f. exp(x/(1 - x^3)^(1/3)).

%F a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n/3-1,k)/(n-3*k)!.

%F a(n) == 1 mod 8.

%o (PARI) a(n) = n!*sum(k=0, n\3, binomial(n/3-1, k)/(n-3*k)!);

%Y Cf. A293493, A373518.

%Y Cf. A373522.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Jun 08 2024