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 A037963 #15 Jun 20 2022 04:29:38
%S A037963 0,1,126,5796,186480,5103000,129230640,3162075840,76592355840,
%T A037963 1863435974400,45950224320000,1155068769254400,29708792431718400,
%U A037963 783699448602470400,21234672840116736000,591499300737945600000
%N A037963 a(n) = n^2*(n+1)*(3*n^2 + 7*n - 2)*(n+5)!/11520.
%C A037963 For n>=1, a(n) is equal to the number of surjections from {1,2,...,n+5} onto {1,2,...,n}. - Aleksandar M. Janjic and _Milan Janjic_, Feb 24 2007
%D A037963 Identity (1.21) in H. W. Gould, Combinatorial Identities, Morgantown, 1972; page 3.
%H A037963 G. C. Greubel, <a href="/A037963/b037963.txt">Table of n, a(n) for n = 0..350</a>
%H A037963 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%F A037963 From _G. C. Greubel_, Jun 20 2022: (Start)
%F A037963 a(n) = (-1)^n * Sum_{j=0..n} (-1)^j * binomial(n, j)*j^(n+5).
%F A037963 a(n) = n!*StirlingS2(n+5, n).
%F A037963 a(n) = A131689(n+5, n).
%F A037963 a(n) = A019538(n+5, n).
%F A037963 E.g.f.: x*(1 + 52*x + 328*x^2 + 444*x^3 + 120*x^4)/(1-x)^11. (End)
%t A037963 Table[n!*StirlingS2[n+5, n], {n,0,30}] (* _G. C. Greubel_, Jun 20 2022 *)
%o A037963 (Magma) [Factorial(n)*StirlingSecond(n+5,n): n in [0..30]]; // _G. C. Greubel_, Jun 20 2022
%o A037963 (SageMath) [factorial(n)*stirling_number2(n+5,n) for n in (0..30)] # _G. C. Greubel_, Jun 20 2022
%Y A037963 Cf. A000142, A019538, A112494, A131689.
%K A037963 nonn
%O A037963 0,3
%A A037963 _N. J. A. Sloane_