A365982 - OEIS

%I #12 Sep 24 2023 09:16:42

%S 1,0,0,2,0,0,80,0,5040,13440,0,3326400,5913600,479001600,3632428800,

%T 5381376000,1399882176000,6586804224000,364469833728000,

%U 5019809832576000,18772392038400000,2898136435138560000,24517466017228800000,1203790902897623040000

%N Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+3) / (5*k+3) ).

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/5)} (5*k+2)! * binomial(n,5*k+3) * a(n-5*k-3).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+3)/(5*k+3)))))

%Y Cf. A355284, A365980, A365981.

%Y Cf. A365912, A365974.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 24 2023