A341056 - OEIS

%I #22 Feb 14 2021 08:29:52

%S 1,2,9,106,2801,132426,9705577,1015001954,143392421601,26298332570386,

%T 6074043257989001,1724846814877790682,590605908915568818769,

%U 239956225437223244619866,114123836188192016600789481,62808518765936960824453590226,39603421893790601518269204039617

%N a(n) = n! * [x^n] exp(x/(1 - n*x)) / (1 - x).

%F a(n) = n! * Sum_{k=0..n} A341033(k,n)/k! = n! * (1 + Sum_{j=1.. n} Sum_{k=1.. j} n^(j-k) * binomial(j-1,k-1)/k!).

%F a(n) ~ BesselI(1,2) * n! * n^(n-1). - _Vaclav Kotesovec_, Feb 14 2021

%e a(3) = 3! * (1 + 1/1! + 7/2! + 73/3!) = 106.

%t Table[n!*(1 + Sum[Sum[n^(j-k)*Binomial[j-1, k-1]/k!, {k, 1, j}], {j, 1, n}]), {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 14 2021 *)

%o (PARI) {a(n) = n!*(1+sum(j=1, n, sum(k=1, j, n^(j-k)*binomial(j-1, k-1)/k!)))}

%Y Cf. A277373, A293146, A330260, A331658, A341033.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 04 2021