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 A327027 #14 Mar 24 2020 12:37:03
%S A327027 1,0,1,0,1,3,0,1,10,30,0,1,33,315,630,0,1,102,2646,15120,22680,0,1,
%T A327027 348,21135,263340,1039500,1247400,0,1,1170,167310,4118400,32432400,
%U A327027 97297200,97297200,0,1,4113,1333080,61757010,871620750,4937832900,11918907000,10216206000
%N A327027 T(n, k) = (1/n) * Sum_{d|n} phi(d) * A241171(n/d, k) for n >= 1, T(0, k) = 0^k. Triangle read by rows for 0 <= k <= n.
%C A327027 We assume A241171 extended to its (0, 0)-based form.
%e A327027 [0] 1;
%e A327027 [1] 0, 1;
%e A327027 [2] 0, 1, 3;
%e A327027 [3] 0, 1, 10, 30;
%e A327027 [4] 0, 1, 33, 315, 630;
%e A327027 [5] 0, 1, 102, 2646, 15120, 22680;
%e A327027 [6] 0, 1, 348, 21135, 263340, 1039500, 1247400;
%e A327027 [7] 0, 1, 1170, 167310, 4118400, 32432400, 97297200, 97297200;
%p A327027 A327027 := (n, k)-> `if`(n=0, 1, (1/n)*add(phi(d)*A241171(n/d, k), d=divisors(n))):
%p A327027 seq(seq(A327027(n,k), k=0..n), n=0..6);
%t A327027 A327027[0, k_] := 1;
%t A327027 A327027[n_, k_] := DivisorSum[n, EulerPhi[#] A241171[n/#, k] &] / n;
%t A327027 Table[A327027[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
%o A327027 (Sage) # uses[DivisorTriangle from A327029, A241171]
%o A327027 DivisorTriangle(euler_phi, A241171, 8, lambda n: 1/n if n > 1 else 1)
%Y A327027 Cf. A327021 (main diagonal), A327026 (row sums), A241171, A327029.
%K A327027 nonn,tabl
%O A327027 0,6
%A A327027 _Peter Luschny_, Aug 20 2019