A347497 Alternating antidiagonal sums of A047920.

1, 1, 2, 5, 21, 105, 636, 4507, 36449, 330947, 3334302, 36913401, 445422501, 5818511965, 81805201736, 1231687676375, 19772907413361, 337146208373847, 6085000404767514, 115897246212304837, 2323089762369102677, 48883749655553977121, 1077440067884422805556

Offset: 0

Author

Alois P. Heinz, Sep 03 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A047920, A347429, A347431.

Programs

Maple

b:= proc(n, k) option remember;
     `if`(k=0, n!, b(n, k-1)-b(n-1, k-1))
    end:
a:= n-> add(b(n-k, k)*(-1)^k, k=0..n/2):
seq(a(n), n=0..23);

Mathematica

b[n_, k_] := b[n, k] = If[k == 0, n!, b[n, k-1] - b[n-1, k-1]];
a[n_] :=  Sum[b[n-k, k]*(-1)^k, {k, 0, n/2}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 05 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * A047920(n-k,k).

a(n) mod 2 = A152822(n).