A349783 a(n) = Sum_{j=0..n} |Stirling1(2*n, j)|.

1, 1, 17, 619, 38009, 3555161, 475971957, 87025015687, 20913570481057, 6401730410889889, 2432850898346888777, 1123996170986262914979, 620447951124750866054313, 403291412174732586716167529, 304888338816008019564815376029, 265252859069372498997243448483215

Offset: 0

Author

Peter Luschny, Dec 09 2021

Keywords

• nonn

Crossrefs

Central terms of A349782.

Cf. A132393.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0, 0,
      add(b(n-j, k-1)*binomial(n-1, j-1)*(j-1)!, j=1..n)))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..15);  # Alois P. Heinz, Dec 09 2021

Mathematica

a[n_] := Sum[Abs[StirlingS1[2*n, j]], {j, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Dec 09 2021 *)

PARI

a(n) = sum(j=0, n, abs(stirling(2*n, j, 1))); \\ Michel Marcus, Dec 09 2021

Python

from sympy.functions.combinatorial.numbers import stirling
def A349783(n): return sum(abs(stirling(2*n,j,kind=1)) for j in range(n+1)) # Chai Wah Wu, Dec 09 2021

Formula

a(n) = Sum_{j=0..n} A132393(2n,j). - Alois P. Heinz, Dec 10 2021