A365908 - OEIS

%I #10 Sep 23 2023 07:28:26

%S 1,0,1,0,6,1,90,42,2521,2268,113742,166321,7543206,16218930,691242553,

%T 2044833336,83708046246,324830941345,12951273345282,63596620804122,

%U 2493395633726425,15062005915534116,584749646165678622,4247497704703187089,164155618660742879022

%N Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+2) / (3*k+2)! ).

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+2)/(3*k+2)!))))

%Y Cf. A032032, A365909.

%Y Cf. A365338.

%K nonn,easy

%O 0,5

%A _Seiichi Manyama_, Sep 22 2023