A347429 a(n) is the alternating sum of the n-th row of A047920.

1, 1, 2, 3, 18, 47, 516, 1851, 28502, 128943, 2546352, 13889291, 334552866, 2135390367, 60692391308, 443650121787, 14531752130766, 119684543973551, 4438679955367752, 40666524402277323, 1684291581885909722, 16989963249272202591, 777243725319000331236

Offset: 0

Author

Alois P. Heinz, Sep 01 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A047920.

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)*(-1)^k, k=0..n):
seq(a(n), n=0..23);

Mathematica

a[n_] := Sum[(-1)^(j+k)*Binomial[k, j]*(n-j)!, {j, 0, n}, {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 04 2022 *)

PARI

row(n) = vector(n+1, k, k--; sum(j=0, n, (-1)^j * binomial(k, j)*(n-j)!)); \\ A047920
a(n) = my(v=row(n)); sum(k=1, n+1, (-1)^k*row[k]); \\ Michel Marcus, Sep 04 2021

Formula

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