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 A047797 #23 Jan 10 2025 12:37:27
%S A047797 1,1,2,11,87,952,13513,237113,5016728,125121009,3615047527,
%T A047797 119384499720,4455637803543,186152008588691,8636436319397292,
%U A047797 441871067839416319,24781002306869712365,1515279889256750470086,100546673139756241189021
%N A047797 a(n) = Sum_{k=0..n} Stirling2(n,k)^2.
%C A047797 If S is the lower matrix of Stirling numbers of the second kind, this sequence (without the first term 1) is the diagonal of the matrix S.Transpose[S]. - _Sergio Falcon_, May 02 2007
%H A047797 G. C. Greubel, <a href="/A047797/b047797.txt">Table of n, a(n) for n = 0..320</a>
%p A047797 seq(add(Stirling2(n, k)^2, k = 0..n), n = 0..20); # _G. C. Greubel_, Aug 07 2019
%t A047797 Table[Sum[StirlingS2[n,k]^2,{k,0,n}],{n,0,20}] (* _Emanuele Munarini_, Jul 01 2011 *)
%o A047797 (Maxima) makelist(sum(stirling2(n,k)^2,k,0,n),n,0,20); /* _Emanuele Munarini_, Jul 01 2011 */
%o A047797 (PARI) {a(n) = sum(k=0,n, stirling(n,k,2)^2)};
%o A047797 vector(20, n, n--; a(n)) \\ _G. C. Greubel_, Aug 07 2019
%o A047797 (Magma) [(&+[StirlingSecond(n,k)^2: k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 07 2019
%o A047797 (Sage) [sum(stirling_number2(n,k)^2 for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Aug 07 2019
%o A047797 (GAP) List([0..20], n-> Sum([0..n], k-> Stirling2(n,k)^2 )); # _G. C. Greubel_, Aug 07 2019
%Y A047797 Cf. A008277, A047796, A342110.
%K A047797 nonn
%O A047797 0,3
%A A047797 _N. J. A. Sloane_