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

1,2

Links

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

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A094416.

Sequence in context: A090226 A355672 A356597 * A346545 A179513 A302896

Adjacent sequences: A094419 A094420 A094421 * A094423 A094424 A094425

Keyword

nonn

Author

Ralf Stephan, May 02 2004

Status

approved