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 A363916 #7 Jul 05 2023 08:25:40
%S A363916 1,0,1,0,1,1,0,0,2,1,0,0,2,3,1,0,0,6,6,4,1,0,0,12,24,12,5,1,0,0,30,72,
%T A363916 60,20,6,1,0,0,54,240,240,120,30,7,1,0,0,126,696,1020,600,210,42,8,1,
%U A363916 0,0,240,2184,4020,3120,1260,336,56,9,1
%N A363916 Array read by descending antidiagonals. A(n, k) = Sum_{d=0..k} A363914(k, d) * n^d.
%C A363916 Row n gives the number of n-ary sequences with primitive period k.
%C A363916 See A074650 and A143324 for combinatorial interpretations.
%H A363916 E. N. Gilbert and J. Riordan, <a href="http://projecteuclid.org/euclid.ijm/1255631587">Symmetry types of periodic sequences</a>, Illinois J. Math., 5 (1961), 657-665.
%F A363916 If k > 0 then k divides A(n, k), see the transposed array of A074650.
%F A363916 If k > 0 then n divides A(n, k), see the transposed array of A143325.
%e A363916 Array A(n, k) starts:
%e A363916 [0] 1, 0, 0, 0, 0, 0, 0, 0, 0, ... A000007
%e A363916 [1] 1, 1, 0, 0, 0, 0, 0, 0, 0, ... A019590
%e A363916 [2] 1, 2, 2, 6, 12, 30, 54, 126, 240, ... A027375
%e A363916 [3] 1, 3, 6, 24, 72, 240, 696, 2184, 6480, ... A054718
%e A363916 [4] 1, 4, 12, 60, 240, 1020, 4020, 16380, 65280, ... A054719
%e A363916 [5] 1, 5, 20, 120, 600, 3120, 15480, 78120, 390000, ... A054720
%e A363916 [6] 1, 6, 30, 210, 1260, 7770, 46410, 279930, 1678320, ... A054721
%e A363916 [7] 1, 7, 42, 336, 2352, 16800, 117264, 823536, 5762400, ... A218124
%e A363916 [8] 1, 8, 56, 504, 4032, 32760, 261576, 2097144, 16773120, ... A218125
%e A363916 A000012|A002378| A047928 | A218130 | A218131
%e A363916 A001477,A007531, A061167, A133499, (diagonal A252764)
%e A363916 .
%e A363916 Triangle T(n, k) starts:
%e A363916 [0] 1;
%e A363916 [1] 0, 1;
%e A363916 [2] 0, 1, 1;
%e A363916 [3] 0, 0, 2, 1;
%e A363916 [4] 0, 0, 2, 3, 1;
%e A363916 [5] 0, 0, 6, 6, 4, 1;
%e A363916 [6] 0, 0, 12, 24, 12, 5, 1;
%e A363916 [7] 0, 0, 30, 72, 60, 20, 6, 1;
%e A363916 [8] 0, 0, 54, 240, 240, 120, 30, 7, 1;
%p A363916 A363916 := (n, k) -> local d; add(A363914(k, d) * n^d, d = 0 ..k):
%p A363916 for n from 0 to 9 do seq(A363916(n, k), k = 0..8) od;
%o A363916 (SageMath)
%o A363916 def A363916(n, k): return sum(A363914(k, d) * n^d for d in range(k + 1))
%o A363916 for n in range(9): print([A363916(n, k) for k in srange(9)])
%o A363916 def T(n, k): return A363916(k, n - k)
%Y A363916 Variant: A143324.
%Y A363916 Rows: A000007 (n=0), A019590 (n=1), A027375 (n=2), A054718 (n=3), A054719 (n=4), A054720, A054721, A218124, A218125.
%Y A363916 Columns: A000012 (k=0), A001477 (k=1), A002378 (k=2), A007531(k=3), A047928, A061167, A218130, A133499, A218131.
%Y A363916 Cf. A252764 (main diagonal), A074650, A363914.
%K A363916 nonn,tabl
%O A363916 0,9
%A A363916 _Peter Luschny_, Jul 04 2023