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 A334896 #7 May 27 2020 21:47:26
%S A334896 648,648,686,12096,12096,686,192000,139968,192000,139968,1866240,
%T A334896 179712,179712,1866240,814968,2101248,102036672,331776000,102036672,
%U A334896 331776000,2101248,814968,179712000,4423680000,1866240000,131010048,179712000,4423680000,1866240000,131010048
%N A334896 Read terms e = T(n,k) in A333624 as Product(prime(k)^e) for n in A334769.
%C A334896 Row a(n) of A067255 = row A334769(n) of A333624.
%C A334896 An XOR-triangle t(n) is an inverted 0-1 triangle formed by choosing a top row the binary rendition of n and having each entry in subsequent rows be the XOR of the two values above it, i.e., A038554(n) applied recursively until we reach a single bit.
%C A334896 Let T(n,k) address the terms in the k-th position of row n in A333624.
%C A334896 This sequence encodes T(n,k) via A067255 to succinctly express the number of zero-triangles in A334769(n). To decode a(n) => A333624(A334769(n)), we use A067255(a(n)).
%H A334896 Michael De Vlieger, <a href="/A334896/b334896.txt">Table of n, a(n) for n = 1..10000</a>
%H A334896 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A334896 <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>
%e A334896 a(1) = 648, since b(A334769(1)) = b(151) = 10010111, which generates T(151) as shown below, replacing 1 with "@" and 0 with ".":
%e A334896 @ . . @ . @ @ @
%e A334896 @ . @ @ @ . .
%e A334896 @ @ . . @ .
%e A334896 . @ . @ @
%e A334896 @ @ @ .
%e A334896 . . @
%e A334896 . @
%e A334896 @
%e A334896 In this figure we see 3 zero-triangles of side length k = 1, and 4 of side length k = 2, therefore, T(1,1) = 3 and T(1,2) = 4. This becomes 2^3 * 3^4 = 8 * 81 = 648.
%e A334896 Relationship of this sequence to A334556 and A333624:
%e A334896 n A334769(n) a(n) Row n of A333624
%e A334896 --------------------------------------
%e A334896 1 151 648 3, 4
%e A334896 2 233 648 3, 4
%e A334896 3 543 686 1, 0, 0, 3
%e A334896 4 599 12096 6, 3, 0, 1
%e A334896 5 937 12096 6, 3, 0, 1
%e A334896 6 993 686 1, 0, 0, 3
%e A334896 7 1379 192000 9, 1, 3
%e A334896 8 1483 139968 6, 7
%e A334896 9 1589 192000 9, 1, 3
%e A334896 10 1693 139968 6, 7
%e A334896 11 2359 1866240 9, 6, 1
%e A334896 12 2391 179712 9, 3, 0, 0, 0, 1
%e A334896 13 3753 179712 9, 3, 0, 0, 0, 1
%e A334896 14 3785 1866240 9, 6, 1
%e A334896 15 8607 814968 3, 3, 0, 3, 1
%e A334896 16 9559 2101248 12, 3, 0, 0, 0, 0, 0, 1
%e A334896 ...
%t A334896 With[{s = Rest[Import["https://oeis.org/A334769/b334769.txt", "Data"][[All, -1]]]}, Map[With[{w = NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &]}, If[Length@ # == 0, 1, Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, #] &@ ReplacePart[ConstantArray[0, Max@ #[[All, 1]]], Map[#1 -> #2 & @@ # &, #]]] &@ Tally@ Flatten@ Array[If[# == 1, Map[If[First@ # == 1, Nothing, Length@ #] &, Split@ w[[#]]], Map[If[First@ # == -1, Length@ #, Nothing] &, Split[w[[#]] - Most@ w[[# - 1]]]]] &, Length@ w]] /. -Infinity -> 0 &, s[[1 ;; 29]]]]
%Y A334896 Cf. A038554, A067255, A070939, A333624, A334591, A334556, A334769.
%K A334896 nonn
%O A334896 1,1
%A A334896 _Michael De Vlieger_, May 23 2020