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 A167892 #33 Feb 16 2025 08:33:11
%S A167892 1,5,30,226,1990,19414,203455,2248355,25887399,307993015,3763786811,
%T A167892 47032778955,598933188955,7751562502555,101741582076580,
%U A167892 1351906409905480,18159677984049580,246298405721739580,3369517588450715680,46457194476711692080
%N A167892 a(n) = Sum_{k=1..n} Catalan(k)^2.
%C A167892 CatalanNumber(k) = (2k)!/(k!*(k+1)!) = binomial(2k,k)/(k+1).
%H A167892 G. C. Greubel, <a href="/A167892/b167892.txt">Table of n, a(n) for n = 1..500</a>
%H A167892 Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Barry/barry321.html">Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices</a>, Journal of Integer Sequences, 19, 2016, #16.3.5.
%H A167892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>
%F A167892 a(n) = Sum_{k=1..n} Catalan(k)^2.
%F A167892 a(n) = Sum_{k=1..n} ((2k)!/(k!*(k+1)!))^2.
%F A167892 a(n) = Sum_{k=1..n} A000108(k)^2.
%F A167892 a(n) = Sum_{k=1..n} A001246(k).
%F A167892 a(n) = A094639(n) - 1.
%F A167892 G.f.: (Hypergeometric2F1(-1/2,-1/2,1,16*x) - 4*x - 1)/(4*x*(1 - x)). - _Ilya Gutkovskiy_, Jul 01 2016
%t A167892 Array[n \[Function] Sum[CatalanNumber[k]^2, {k, 1, n}], 20] (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010 *)
%t A167892 Accumulate[CatalanNumber[Range[1, 20]]^2] (* _Vincenzo Librandi_, Jul 01 2016 *)
%o A167892 (Magma) [&+[Catalan(i)^2: i in [1..n]]: n in [1..20]]; // _Vincenzo Librandi_, Jul 01 2016
%Y A167892 Cf. A000108, A014138, A167892, A167893, A001246, A033536, A014137, A094639.
%K A167892 nonn
%O A167892 1,2
%A A167892 _Alexander Adamchuk_, Nov 15 2009
%E A167892 More terms from J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010