cp's OEIS Frontend

A340823 a(n) = exp(-1) * Sum_{k>=0} (k*(k - n))^n / k!.

%I A340823 #10 Jun 13 2024 01:47:50
%S A340823 1,1,3,5,124,-2075,91993,-4709903,312334595,-25531783799,
%T A340823 2524083665172,-296260739274275,40667620527027177,
%U A340823 -6446882734412545043,1167717545574222779643,-239452569059443831797303,55146244227862697483251020,-14163492441645773105212592623
%N A340823 a(n) = exp(-1) * Sum_{k>=0} (k*(k - n))^n / k!.
%H A340823 G. C. Greubel, <a href="/A340823/b340823.txt">Table of n, a(n) for n = 0..260</a>
%F A340823 a(n) = Sum_{k=0..n} binomial(n,k) * Bell(2*n-k) * (-n)^k.
%t A340823 Table[Exp[-1] Sum[(k (k - n))^n/k!, {k, 0, Infinity}], {n, 0, 17}]
%t A340823 Join[{1}, Table[Sum[Binomial[n, k] BellB[2 n - k] (-n)^k, {k, 0, n}], {n, 1, 17}]]
%o A340823 (Magma)
%o A340823 A340823:= func< n | (&+[(-n)^j*Binomial(n,j)*Bell(2*n-j): j in [0..n]]) >;
%o A340823 [A340823(n): n in [0..30]]; // _G. C. Greubel_, Jun 12 2024
%o A340823 (SageMath)
%o A340823 def A340823(n): return sum( binomial(n,k)*bell_number(2*n-k)*(-n)^k for k in range(n+1))
%o A340823 [A340823(n) for n in range(31)] # _G. C. Greubel_, Jun 12 2024
%Y A340823 Cf. A000110, A020556, A020557, A290219, A334243, A340822.
%K A340823 sign
%O A340823 0,3
%A A340823 _Ilya Gutkovskiy_, Jan 22 2021