%I #17 Nov 23 2021 09:44:30

%S 1,1,4,20,126,937,7938,74909,775022,8688827,104608026,1342844846,

%T 18273663268,262347913479,3957524475778,62511713866200,

%U 1030842278673510,17700339693712731,315740112103311666,5839137279831300536,111749137533005481700,2209538389126578658875

%N a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^(n-k).

%t Join[{1}, Table[Sum[Binomial[n, j]*CatalanNumber[j]*j^(n-j), {j, 0, n}], {n, 1, 25}]]

%o (PARI) a(n) = sum(k=0, n, binomial(n,k)*(binomial(2*k,k)/(k+1))*k^(n-k)); \\ _Michel Marcus_, Nov 23 2021

%Y Cf. A000248, A007317, A064613, A104455, A104498, A154623, A292632.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Nov 23 2021