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 A380707 #40 May 23 2025 03:15:18
%S A380707 1,3,74,4578,520024,93638820,24469489008,8744195444880,
%T A380707 4093736159733120,2430707964048640800,1784480276787736636800,
%U A380707 1586934417435493101528960,1680937045347184025188838400,2091005717306225140393765228800,3018259634660179964662904164915200
%N A380707 a(n) = [x^n] Product_{k=0..n} (1 + (n^2+k)*x).
%F A380707 a(n) = A165675((n+1)*n,n^2).
%F A380707 a(n) = Sum_{k=0..n} (k+1) * n^(2*k) * |Stirling1(n+1,k+1)|.
%F A380707 a(n) = (n+1)! * Sum_{k=0..n} (-1)^k * binomial(-n^2,k)/(n+1-k).
%F A380707 a(n) = ((n+1)*n)!/(n^2)! * (1 + n^2 * Sum_{k=1..n} 1/(n^2+k)).
%F A380707 a(n) ~ exp(1/2) * n^(2*n+1). - _Vaclav Kotesovec_, May 23 2025
%t A380707 Table[SeriesCoefficient[Product[1 + (n^2+k)*x, {k, 0, n}], {x, 0, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, May 23 2025 *)
%o A380707 (PARI) a(n) = sum(k=0, n, (k+1)*n^(2*k)*abs(stirling(n+1, k+1, 1)));
%Y A380707 Main diagonal of A382347.
%Y A380707 Cf. A165675.
%K A380707 nonn
%O A380707 0,2
%A A380707 _Seiichi Manyama_, May 18 2025