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

0,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A047920.

Sequence in context: A064777 A137784 A053195 * A211867 A003693 A216628

Adjacent sequences: A347426 A347427 A347428 * A347430 A347431 A347432

Keyword

nonn

Author

Alois P. Heinz, Sep 01 2021

Status

approved