A391311 a(n) = Sum_{k=0..n} HurwitzZeta(k-n, k) - HurwitzZeta(k-n, n).

0, 0, 2, 16, 150, 1782, 26180, 458862, 9326848, 215384572, 5565571766, 159040991124, 4978740691786, 169424173777626, 6226621358218824, 245777981105854834, 10369733004076891156, 465705290633776793136, 22180678238507766642618, 1116705974207049494434152, 59256223529491162894126814

Offset

0,3

Comments

All the terms are even.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) ~ n^n / (exp(1) - 1). - Vaclav Kotesovec, Dec 06 2025

Mathematica

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

Prog

(PARI) a(n) = sum(k=0, n, sum(i=0, n-k-1, (k+i)^(n-k))); \\ Michel Marcus, Dec 10 2025

Crossrefs

Antidiagonal sums of A391310.

Twice A391313.

Sequence in context: A337793 A103885 A262266 * A124578 A332566 A085510

Adjacent sequences: A391308 A391309 A391310 * A391312 A391313 A391314

Keyword

nonn

Author

Stefano Spezia, Dec 06 2025

Status

approved