A391313 a(n) = ( Sum_{k=0..n} HurwitzZeta(k-n, k) - HurwitzZeta(k-n, n) ) / 2.

0, 0, 1, 8, 75, 891, 13090, 229431, 4663424, 107692286, 2782785883, 79520495562, 2489370345893, 84712086888813, 3113310679109412, 122888990552927417, 5184866502038445578, 232852645316888396568, 11090339119253883321309, 558352987103524747217076, 29628111764745581447063407

Offset

0,4

Links

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

Formula

a(n) ~ n^n / (2*exp(1) - 2). - Vaclav Kotesovec, Dec 06 2025

Mathematica

a[n_]:=Sum[HurwitzZeta[k-n, k]-HurwitzZeta[k-n, n], {k, 0, n}]/2; Array[a, 21, 0]

Prog

(PARI) a(n) = sum(k=0, n, sum(i=0, n-k-1, (k+i)^(n-k)))/2; \\ Michel Marcus, Dec 12 2025

Crossrefs

Half A391311.

Cf. A391310.

Sequence in context: A361528 A261065 A071720 * A273998 A111685 A302814

Adjacent sequences: A391310 A391311 A391312 * A391314 A391315 A391316

Keyword

nonn

Author

Stefano Spezia, Dec 06 2025

Status

approved