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 A123618 #8 Oct 26 2017 18:58:12
%S A123618 1,4,39,392,4420,52272,644231,8179600,106376580,1410528080,
%T A123618 19006875580,259613952864,3587352778256,50068405195200,
%U A123618 704925148185495,10001318622631200,142866058397606500,2053248549639210000
%N A123618 a(n) = A123610(2*n+2,n).
%C A123618 Related sequences: A123610(2n,n) = A123617(n); A123610(2n+1,n) = A000891(n); A123610(2n+2,n)/(n+1) = A123619(n). a(n) is divisible by (n+1): a(n)/(n+1) = A123619(n).
%H A123618 G. C. Greubel, <a href="/A123618/b123618.txt">Table of n, a(n) for n = 0..830</a>
%t A123618 T[_, 0] = 1; T[n_, k_] := 1/n DivisorSum[n, If[GCD[k, #] == #, EulerPhi[#]*Binomial[n/#, k/#]^2, 0] &];
%t A123618 Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* A123610 *)
%t A123618 Table[T[2*n, n], {n, 0, 50}] (* A123617 *)
%t A123618 Table[T[2*n + 2, n], {n, 0, 50}] (* A123618 *)
%t A123618 Table[T[2*n + 2,n]/(n+1), {n, 0, 50}] (* A123619 *)
%t A123618 (* _G. C. Greubel_, Oct 26 2017 *)
%o A123618 (PARI) {a(n)=if(n==0,1,(1/(2*n+2))*sumdiv(2*n+2,d,if(gcd(n,d)==d, eulerphi(d)*binomial((2*n+2)/d,n/d)^2,0)))}
%Y A123618 Cf. A123610 (triangle); A123617, A000891, A123619.
%K A123618 nonn
%O A123618 0,2
%A A123618 _Paul D. Hanna_, Oct 03 2006