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 A322627 #12 Jan 26 2019 11:17:57
%S A322627 1,4,55,1260,40593,1690920,86550035,5260335080,370410456273,
%T A322627 29664913887180,2663386839535695,265000164136279572,
%U A322627 28945346029081686865,3443628513369917505360,443271719760096505911675,61385459345641259759898000,9100387546322497725789848865,1438068852777042379374392377620,241308826278118770656171323634855,42852242077203438281471161279058300
%N A322627 a(n) = [y^(n+1)] (n + y) * Product_{k=1..2*n} (k + y), for n >= 0.
%C A322627 A diagonal in triangle A268647: a(n) = A268647(n, n+1) for n >= 0.
%H A322627 Paul D. Hanna, <a href="/A322627/b322627.txt">Table of n, a(n) for n = 0..300</a>
%e A322627 The coefficients of y^k in (n + y) * Product_{j=1..2*n} (j + y), for k=0..2*n+1, yields row n of triangle A268647, which begins:
%e A322627 0, 1;
%e A322627 2, 5, 4, 1;
%e A322627 48, 124, 120, 55, 12, 1;
%e A322627 2160, 6012, 6636, 3829, 1260, 238, 24, 1;
%e A322627 161280, 478656, 582080, 387260, 157080, 40593, 6720, 690, 40, 1;
%e A322627 18144000, 56772000, 74396520, 54801076, 25494150, 7927205, 1690920, 248523, 24750, 1595, 60, 1; ...
%e A322627 this sequence is the diagonal a(n) = A268647(n, n+1) for n >= 0.
%o A322627 (PARI) /* a(n) = [y^(n+1)] (n + y)*Product_{k=1..2*n} (k + y) */
%o A322627 {A268647(n, k) = polcoeff((n + y)*prod(k=1, 2*n, k + y), k, y)}
%o A322627 {a(n) = A268647(n, n+1)}
%o A322627 for(n=0, 25, print1(a(n),", "));
%Y A322627 Cf. A268647.
%K A322627 nonn
%O A322627 0,2
%A A322627 _Paul D. Hanna_, Jan 26 2019