A357920 - OEIS

%I #8 Oct 20 2022 12:44:40

%S 1,0,0,0,0,1,-1,2,-6,24,-119,717,-5029,40270,-362606,3627037,

%T -39903738,478892051,-6225994449,87167664184,-1307553837291,

%U 20921303563234,-355667626509575,6402090252833481,-121640761396741607,2432831275825738669,-51089718792714854191

%N a(n) = Sum_{k=0..floor(n/5)} Stirling1(n - 4*k,k).

%F G.f.: Sum_{k>=0} (-x)^k * Product_{j=0..k-1} (j - x^4).

%o (PARI) a(n) = sum(k=0, n\5, stirling(n-4*k, k, 1));

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k*prod(j=0, k-1, j-x^4)))

%Y Cf. A357902, A357919.

%K sign

%O 0,8

%A _Seiichi Manyama_, Oct 20 2022