A349639 a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^k.

1, 2, 11, 163, 4177, 150606, 7002679, 399296682, 26997867705, 2112814307980, 187919721166951, 18727570061711897, 2067435790679136937, 250474099952311886236, 33043529154916822685459, 4715582224589290429430011, 723854564711343436767660481, 118933484485939500023357177356

Offset: 0

Author

Vaclav Kotesovec, Nov 23 2021

Keywords

• nonn

Crossrefs

Cf. A007317, A064613, A291699, A292632, A349603, A349640.

Programs

Mathematica

Table[1+Sum[Binomial[n, j]*CatalanNumber[j]*j^j, {j, 1, n}], {n, 0, 20}]

PARI

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

Formula

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...