A365989 - OEIS

%I #9 Sep 25 2023 07:47:05

%S 1,0,0,0,6,0,0,0,1260,40320,0,0,1247400,172972800,6227020800,0,

%T 3405402000,1235025792000,153848927232000,6402373705728000,

%U 19799007228000,14783258730240000,4243499220280320000,545332851008225280000,25852227123135781368000

%N Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+4) / (5*k+4) ).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-4)/5)} a(n-5*k-4)/(n-5*k-4)!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+4)/(5*k+4)))))

%Y Cf. A365969, A365972, A365974.

%Y Cf. A365895, A365990.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 25 2023