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

%I A347429 #15 Jun 04 2022 04:34:25
%S A347429 1,1,2,3,18,47,516,1851,28502,128943,2546352,13889291,334552866,
%T A347429 2135390367,60692391308,443650121787,14531752130766,119684543973551,
%U A347429 4438679955367752,40666524402277323,1684291581885909722,16989963249272202591,777243725319000331236
%N A347429 a(n) is the alternating sum of the n-th row of A047920.
%H A347429 Alois P. Heinz, <a href="/A347429/b347429.txt">Table of n, a(n) for n = 0..450</a>
%F A347429 a(n) = Sum_{k=0..n} (-1)^k * A047920(n,k).
%p A347429 b:= proc(n, k) option remember;
%p A347429      `if`(k=0, n!, b(n, k-1)-b(n-1, k-1))
%p A347429     end:
%p A347429 a:= n-> add(b(n, k)*(-1)^k, k=0..n):
%p A347429 seq(a(n), n=0..23);
%t A347429 a[n_] := Sum[(-1)^(j+k)*Binomial[k, j]*(n-j)!, {j, 0, n}, {k, 0, n}];
%t A347429 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jun 04 2022 *)
%o A347429 (PARI) row(n) = vector(n+1, k, k--; sum(j=0, n, (-1)^j * binomial(k, j)*(n-j)!)); \\ A047920
%o A347429 a(n) = my(v=row(n)); sum(k=1, n+1, (-1)^k*row[k]); \\ _Michel Marcus_, Sep 04 2021
%Y A347429 Cf. A047920.
%K A347429 nonn
%O A347429 0,3
%A A347429 _Alois P. Heinz_, Sep 01 2021