A355292 a(n) = Sum_{k=1..n} |Stirling1(n,k)| * Catalan(k-1).

1, 2, 7, 34, 208, 1521, 12871, 123306, 1316316, 15471114, 198319614, 2751524557, 41058030388, 655427422651, 11142214939181, 200919300509214, 3829751956014084, 76928721540858772, 1624015067086462504, 35942784684670110710, 832134062464902004336

Offset: 1

Author

Seiichi Manyama, Jun 27 2022

Keywords

• nonn

Crossrefs

Cf. A000108, A052851, A086662.

Programs

Mathematica

Table[Sum[Abs[StirlingS1[n,k]] * CatalanNumber[k-1], {k,1,n}], {n,1,20}] (* Vaclav Kotesovec, Jul 01 2022 *)

PARI

a(n) = sum(k=1, n, abs(stirling(n, k, 1))*binomial(2*k-2, k-1)/k);