This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347497 #12 Jun 05 2022 03:39:45
%S A347497 1,1,2,5,21,105,636,4507,36449,330947,3334302,36913401,445422501,
%T A347497 5818511965,81805201736,1231687676375,19772907413361,337146208373847,
%U A347497 6085000404767514,115897246212304837,2323089762369102677,48883749655553977121,1077440067884422805556
%N A347497 Alternating antidiagonal sums of A047920.
%H A347497 Alois P. Heinz, <a href="/A347497/b347497.txt">Table of n, a(n) for n = 0..450</a>
%F A347497 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * A047920(n-k,k).
%F A347497 a(n) mod 2 = A152822(n).
%p A347497 b:= proc(n, k) option remember;
%p A347497 `if`(k=0, n!, b(n, k-1)-b(n-1, k-1))
%p A347497 end:
%p A347497 a:= n-> add(b(n-k, k)*(-1)^k, k=0..n/2):
%p A347497 seq(a(n), n=0..23);
%t A347497 b[n_, k_] := b[n, k] = If[k == 0, n!, b[n, k-1] - b[n-1, k-1]];
%t A347497 a[n_] := Sum[b[n-k, k]*(-1)^k, {k, 0, n/2}];
%t A347497 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jun 05 2022, after _Alois P. Heinz_ *)
%Y A347497 Cf. A047920, A347429, A347431.
%K A347497 nonn
%O A347497 0,3
%A A347497 _Alois P. Heinz_, Sep 03 2021