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 A037972 #37 Jun 22 2022 07:54:10
%S A037972 0,1,12,108,800,5250,31752,181104,988416,5212350,26741000,134132856,
%T A037972 660284352,3199016548,15288882000,72209880000,337535723520,
%U A037972 1563410094390,7182839945160,32761238433000,148450107960000,668693511305820,2995943329133040,13356820221694560
%N A037972 a(n) = n^2*(n+1)*binomial(2*n-2, n-1)/2.
%D A037972 Identity (3.78), S_{3}, in H. W. Gould, Combinatorial Identities, Morgantown, 1972, page 31.
%H A037972 Seiichi Manyama, <a href="/A037972/b037972.txt">Table of n, a(n) for n = 0..1000</a>
%F A037972 a(n) = Sum_{k=0..n} k^3*(C(n,k))^2. [heruneedollar (heruneedollar(AT)gmail.com), Mar 20 2010]
%F A037972 a(n) = A000217(n)*A037965(n). - _R. J. Mathar_, Jul 26 2015
%F A037972 (n-1)^2*a(n) = 2*(11*n-16)*a(n-1) + 8*n*(2*n-5)*a(n-2). - _R. J. Mathar_, Oct 20 2015
%F A037972 (n-1)^3*a(n) = 2*n*(n+1)*(2*n-3)*a(n-1). - _R. J. Mathar_, Oct 20 2015
%F A037972 G.f.: x * (1 - 2*x + 10*x^2 - 12*x^3) / (1 - 4*x)^(7/2). - _Ilya Gutkovskiy_, Nov 17 2021
%t A037972 Table[n^2*Binomial[n+1,2]*CatalanNumber[n-1], {n,0,30}] (* _G. C. Greubel_, Jun 22 2022 *)
%o A037972 (PARI) {a(n) = n^2*(n+1)*binomial(2*n-2, n-1)/2} \\ _Seiichi Manyama_, Aug 09 2020
%o A037972 (Magma) [n^2*(n+1)*Binomial(2*n-2, n-1)/2: n in [0..30]]; // _G. C. Greubel_, Jun 22 2022
%o A037972 (SageMath) [n^2*binomial(n+1,2)*catalan_number(n-1) for n in (0..30)] # _G. C. Greubel_, Jun 22 2022
%Y A037972 Cf. A000108, A000217, A037965, A037966, A074334, A329913, A329444.
%K A037972 nonn
%O A037972 0,3
%A A037972 _N. J. A. Sloane_