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 A363397 #7 Jun 02 2023 08:51:49
%S A363397 1,5,32,302,3904,64272,1286144,30313712,822571008,25258008320,
%T A363397 865863532544,32779942009344,1358320701014016,61149815860711424,
%U A363397 2971951570679234560,155090406558662064128,8649258967534890123264,513370937392454603833344
%N A363397 a(n) = Sum_{k=0..n} 2^(n - k) * Sum_{j=0..k} binomial(k, j) * (j + 1)^n. Row sums of A363399.
%F A363397 a(n) ~ sqrt(1 + LambertW(exp(-1))) * n^n / ((1 - LambertW(exp(-1))) * exp(n) * LambertW(exp(-1))^(n+1)). - _Vaclav Kotesovec_, Jun 02 2023
%p A363397 a := n -> add(add(binomial(k, j)*(j + 1)^n, j=0..k)*2^(n - k), k = 0..n):
%p A363397 seq(a(n), n = 0..17);
%t A363397 Table[Sum[2^(n-k) * Sum[Binomial[k, j] * (j+1)^n, {j, 0, k}], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 02 2023 *)
%Y A363397 Cf. A363399.
%K A363397 nonn
%O A363397 0,2
%A A363397 _Peter Luschny_, Jun 02 2023