A349603 a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^(n-k).

1, 1, 4, 20, 126, 937, 7938, 74909, 775022, 8688827, 104608026, 1342844846, 18273663268, 262347913479, 3957524475778, 62511713866200, 1030842278673510, 17700339693712731, 315740112103311666, 5839137279831300536, 111749137533005481700, 2209538389126578658875

Offset: 0

Author

Vaclav Kotesovec, Nov 23 2021

Keywords

• nonn

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = sum(k=0, n, binomial(n,k)*(binomial(2*k,k)/(k+1))*k^(n-k)); \\ Michel Marcus, Nov 23 2021