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 A349639 #11 Nov 23 2021 15:53:13
%S A349639 1,2,11,163,4177,150606,7002679,399296682,26997867705,2112814307980,
%T A349639 187919721166951,18727570061711897,2067435790679136937,
%U A349639 250474099952311886236,33043529154916822685459,4715582224589290429430011,723854564711343436767660481,118933484485939500023357177356
%N A349639 a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^k.
%F A349639 a(n) ~ c * 2^(2*n) * n^(n - 3/2) /sqrt(Pi), where c = Sum_{k>=0} 1/(4^k*k!*exp(k)) = exp(exp(-1)/4) = 1.09633177846412646399584148732...
%t A349639 Table[1+Sum[Binomial[n, j]*CatalanNumber[j]*j^j, {j, 1, n}], {n, 0, 20}]
%o A349639 (PARI) a(n) = sum(k=0, n, binomial(n,k) * (binomial(2*k,k)/(k+1)) * k^k); \\ _Michel Marcus_, Nov 23 2021
%Y A349639 Cf. A007317, A064613, A291699, A292632, A349603, A349640.
%K A349639 nonn
%O A349639 0,2
%A A349639 _Vaclav Kotesovec_, Nov 23 2021