A391311 - OEIS

%I #12 Dec 10 2025 12:19:38

%S 0,0,2,16,150,1782,26180,458862,9326848,215384572,5565571766,

%T 159040991124,4978740691786,169424173777626,6226621358218824,

%U 245777981105854834,10369733004076891156,465705290633776793136,22180678238507766642618,1116705974207049494434152,59256223529491162894126814

%N a(n) = Sum_{k=0..n} HurwitzZeta(k-n, k) - HurwitzZeta(k-n, n).

%C All the terms are even.

%F a(n) ~ n^n / (exp(1) - 1). - _Vaclav Kotesovec_, Dec 06 2025

%t a[n_]:=Sum[HurwitzZeta[k-n,k]-HurwitzZeta[k-n,n],{k,0,n}]; Array[a,21,0]

%o (PARI) a(n) = sum(k=0, n, sum(i=0, n-k-1, (k+i)^(n-k))); \\ _Michel Marcus_, Dec 10 2025

%Y Antidiagonal sums of A391310.

%Y Twice A391313.

%K nonn

%O 0,3

%A _Stefano Spezia_, Dec 06 2025