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 A295612 #12 Feb 16 2025 08:33:52
%S A295612 1,3,40,8105,24053106,1016507243472,622366942086680904,
%T A295612 5608321882919220905812521,752711651805019773658037206391596,
%U A295612 1518219710649896586598445898967340890577318,46343146356260529633020448755386347142785083052620084
%N A295612 a(n) = Sum_{k=0..n} binomial(n+k,k)^k.
%H A295612 Seiichi Manyama, <a href="/A295612/b295612.txt">Table of n, a(n) for n = 0..41</a>
%H A295612 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>
%F A295612 a(n) = Sum_{k=0..n} A046899(n,k)^k.
%F A295612 a(n) ~ 2^(2*n^2) / (exp(1/8) * Pi^(n/2) * n^(n/2)). - _Vaclav Kotesovec_, Nov 25 2017
%t A295612 Table[Sum[Binomial[n + k, k]^k, {k, 0, n}], {n, 0, 10}]
%t A295612 Table[Sum[((n + k)!/(n! k!))^k, {k, 0, n}], {n, 0, 10}]
%o A295612 (PARI) a(n) = sum(k=0, n, binomial(n+k,k)^k); \\ _Michel Marcus_, Nov 25 2017
%Y A295612 Cf. A001700, A046899, A112028, A112029, A167008, A219562, A219563, A219564.
%K A295612 nonn
%O A295612 0,2
%A A295612 _Ilya Gutkovskiy_, Nov 24 2017