A367784 - OEIS

%I #4 Dec 01 2023 15:58:58

%S 1,-2,5,17,17,-8151,-311435,-777974,927723585,82906687673,

%T 1693962380101,-707005824990631,-137258747025993071,

%U -10253960705018807830,1697644859939460151413,803696888217607331079149,148126297324647875348070657,-323461353221296480463456191

%N a(n) = exp(1) * Sum_{k>=0} (-1)^k * (n*k - 1)^n / k!.

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * n^k * A000587(k).

%t Table[n! SeriesCoefficient[Exp[1 - x - Exp[n x]], {x, 0, n}], {n, 0, 17}]

%t Unprotect[Power]; 0^0 = 1; Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k, -1], {k, 0, n}], {n, 0, 17}]

%Y Cf. A000587, A109747, A307066, A307080, A330605, A367743, A367744.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Nov 30 2023