A370511 - OEIS

%I #17 Feb 20 2024 13:47:10

%S 1,1,2,6,25,124,738,5137,40926,367236,3664321,40241168,482282700,

%T 6263450401,87618831730,1313438757210,21003941166601,356910563528412,

%U 6422026243338846,121980432505328545,2438957859604373534,51206341993873093608,1126314833020691642497

%N Expansion of Sum_{k>=0} k! * ( x/(1-x^3) )^k.

%F a(n) = Sum_{k=0..floor(n/3)} (n-3*k)! * binomial(n-2*k-1,k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x/(1-x^3))^k))

%o (PARI) a(n) = sum(k=0, n\3, (n-3*k)!*binomial(n-2*k-1, k));

%Y Cf. A001339, A276080.

%Y Cf. A358493.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Feb 20 2024