A365977 - OEIS

%I #10 Sep 24 2023 09:16:23

%S 1,1,2,6,24,120,840,6720,60480,604800,6652800,83462400,1138233600,

%T 16746912000,264176640000,4444771968000,80719172352000,

%U 1556132497920000,31722198842880000,681437830993920000,15378172899747840000,366025806545817600000

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

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

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

%Y Cf. A296676, A365975, A365976.

%Y Cf. A365969.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 23 2023