This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345876 #25 Oct 03 2021 09:09:24
%S A345876 1,1,8,90,1408,28350,697344,20264244,679313408,25805186550,
%T A345876 1095482736640,51397070440716,2640925289349120,147491783753286700,
%U A345876 8895880971425939456,576279075821454657000,39905347440408027725824,2941534126495441574472870,229966392623413457628168192
%N A345876 a(n) = Sum_{k=0..n} binomial(2*n, n-k) * k^n.
%H A345876 Seiichi Manyama, <a href="/A345876/b345876.txt">Table of n, a(n) for n = 0..360</a>
%F A345876 a(n) ~ 2^(2*n + 1/2) * r^(n+1) * n^n / (sqrt(1 + r^2) * exp(n) * (1 - r^2)^n), where r = 0.647918229029602749602061258113970414114660380467168496836586... is the positive root of the equation (1 + r) = (1 - r)*exp(1/r).
%t A345876 Join[{1}, Table[Sum[Binomial[2*n, n-k]*k^n, {k, 0, n}], {n, 1, 20}]]
%o A345876 (PARI) a(n) = sum(k=0, n, binomial(2*n, n-k) * k^n); \\ _Michel Marcus_, Oct 03 2021
%Y A345876 Cf. A072034, A298851.
%K A345876 nonn
%O A345876 0,3
%A A345876 _Vaclav Kotesovec_, Oct 03 2021