A094422 Antidiagonal sums of array A094416.

1, 5, 26, 174, 1531, 17275, 243092, 4165260, 85133685, 2039546785, 56447550542, 1783865468186, 63766726231791, 2558290237404919, 114418196763735112, 5670168958036693976, 309630356618418661737, 18536683645526372648445

Offset: 1

Author

Ralf Stephan, May 02 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..310

Crossrefs

Cf. A094416.

Programs

Magma

A094422:= func< n | (&+[(&+[Factorial(j)*(n-k+1)^j*StirlingSecond(k,j): j in [0..n]]): k in [1..n]]) >;
[A094422(n): n in [1..25]]; // G. C. Greubel, Jan 11 2024

Mathematica

Table[Sum[Sum[j!*(n - k + 1)^j*StirlingS2[k, j], {j, 0, n}], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jul 23 2018 *)

SageMath

def f(n,k,j): return factorial(j)*(n-k+1)^j*stirling_number2(k,j)
def A094422(n): return sum(sum(f(n,k,j) for j in range(n+1)) for k in range(1,n+1))
[A094422(n) for n in range(1,26)] # G. C. Greubel, Jan 11 2024

Formula

a(n) = Sum_{k=1..n} Bo(n-k+1, k), where Bo(r, n) = A094416(r, n).