A351779 - OEIS

%I #10 Feb 19 2022 13:55:57

%S 1,-1,4,-63,2288,-138525,12381084,-1528482823,249005711296,

%T -51739455340953,13353206066063900,-4190486732316600771,

%U 1571373340568392914288,-693899460077821703051125,356404409990391961980227068,-210670220153918100996704166975

%N a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * (n-k)^k/k!.

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

%o (PARI) a(n) = n!*sum(k=0, n, (-n)^(n-k)*(n-k)^k/k!);

%Y Main diagonal of A351776.

%Y Cf. A351765, A351780.

%K sign

%O 0,3

%A _Seiichi Manyama_, Feb 19 2022