A349852 - OEIS

%I #28 Dec 03 2021 09:54:33

%S 0,1,1,0,2,1,-5,20,-28,-47,525,-2056,3902,9633,-129033,664364,

%T -1837904,-2388687,67004697,-478198544,1994889946,-1669470783,

%U -56929813933,615188040196,-3794477505572,12028579019537,50780206473221,-1172949397924184,10766410530764118

%N Expansion of Sum_{k>=0} k * x^k/(1 + k * x).

%F a(n) = -Sum_{k=0..n} (-k)^(n-k+1).

%t a[n_] := -Sum[(-k)^(n - k + 1), {k, 0, n}]; Array[a, 29, 0] (* _Amiram Eldar_, Dec 02 2021 *)

%o (PARI) a(n, s=1, t=1) = sum(k=0, n, (-k^t)^(n-k)*k^s);

%o (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k*x^k/(1+k*x))))

%Y Cf. A038125, A349853, A349854, A349855, A349859, A349860, A349861.

%K sign

%O 0,5

%A _Seiichi Manyama_, Dec 02 2021