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 A026910 #8 Aug 22 2025 20:18:18
%S A026910 28,154,627,2414,9201,35094,134259,515302,1983678,7656374,29619728,
%T A026910 114822606,445925707,1734610302,6757306947,26358212502,102937963242,
%U A026910 402444721782,1574952822852,6169131608622,24184904949252,94885715007390,372536351222832,1463611239163614,5753766284232606,22632379126906174,89072478723401106
%N A026910 a(n) = A026907(2*n, n-1).
%H A026910 G. C. Greubel, <a href="/A026910/b026910.txt">Table of n, a(n) for n = 1..1000</a>
%F A026910 From _G. C. Greubel_, Aug 22 2025: (Start)
%F A026910 a(n) = n*A000108(n) + 3*(n+2)*A000108(n+2) - 18.
%F A026910 a(n) = binomial(2*n, n-1) + 3*binomial(2*n+4, n+1) - 18.
%F A026910 G.f.: (3 - 9*x + 7*x^2 - 3*x^3 + 2*x^4 - (3 - 3*x + 7*x^2 + 17*x^3 + 12*x^4)*sqrt(1-4*x))/( 2*(1-x)*x^3*sqrt(1-4*x) ).
%F A026910 E.g.f.: 6 - 18*exp(x) - (1/x^2)*exp(2*x)*( 6*x(1-4*x)*BesselI(0, 2*x) - (6 - 12*x + 25*x^2)*BesselI(1, 2*x) ). (End)
%t A026910 Table[n*CatalanNumber[n] +3*(n+2)*CatalanNumber[n+2] -18, {n,40}] (* _G. C. Greubel_, Aug 22 2025 *)
%o A026910 (Magma)
%o A026910 A026910:= func< n | n*Catalan(n) +3*(n+2)*Catalan(n+2) -18 >;
%o A026910 [A026910(n): n in [1..40]]; // _G. C. Greubel_, Aug 22 2025
%o A026910 (SageMath)
%o A026910 def A026910(n): return binomial(2*n,n-1) +3*binomial(2*n+4,n+1) -18
%o A026910 print([A026910(n) for n in range(1,41)]) # _G. C. Greubel_, Aug 22 2025
%Y A026910 Cf. A000108, A026907.
%K A026910 nonn,changed
%O A026910 1,1
%A A026910 _Clark Kimberling_
%E A026910 More terms added by _G. C. Greubel_, Aug 22 2025