A368576 - OEIS

%I #10 Dec 31 2023 10:22:44

%S 0,1,8,45,236,1306,8088,57078,457416,4118031,41182312,453008435,

%T 5436105588,70669378832,989371312216,14840569694868,237449115133392,

%U 4036634957288013,72659429231210568,1380529155393034441,27610583107860731324,579822245265075410934

%N a(n) = n! * Sum_{k=0..n} binomial(k+4,5) / k!.

%F a(0) = 0; a(n) = n*a(n-1) + binomial(n+4,5).

%F E.g.f.: x * (1+2*x+x^2+x^3/6+x^4/120) * exp(x) / (1-x).

%o (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1-x))))

%Y Cf. A007526, A103519, A368574, A368575.

%Y Cf. A000389.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Dec 31 2023