Update:
n = 5;
sa = SparseArray[CellularAutomaton[{Total, {}, 1/2}, {{1}, 0}, n]];
satr = Block[{i = 1}, Transpose[RotateRight[#, n + 1 - i++] & /@
(Riffle[#, {0}] & /@ sa) /. 0 -> ""]] ;
satr // Grid

Original post:
saF = SparseArray[CellularAutomaton[#, {{1}, 0}, #2]][#3] &;
ptF = Function[{n}, saF @@@ {{{Total, {}, 1/2}, n, "NonzeroValues"},
{{Unitize[#[[1]] + #[[3]]] &, {}, 1}, n, "NonzeroPositions"}}];
Row[Grid /@ {#, Transpose@#} &@SparseArray[Rule @@ Reverse[ptF[5]]], Spacer[10]]

Remove 0
s:
Row[(Grid /@ {#, Transpose@#} &@
Normal[SparseArray[Rule @@ Reverse[ptF[5]]]] /. 0 -> ""), Spacer[10]]
Graphics:
Graphics[Thread[Text @@ ({Style[#, 24, Red, Bold] & /@ #, #2} & @@ #)],
AspectRatio -> 3/4] &[ptF[5]]

Graphics[Thread[Text @@ ({Style[#, 24, Red, Bold] & /@ #, Reverse /@ #2} & @@ #)],
AspectRatio -> 3/4] &[ptF[5]]

Graph:
Row[Table[Graph[Range[Length@#1], {}, VertexSize -> {.5, .5}, ImageSize -> 200,
VertexLabels -> Thread[Range[Length@#1] ->
(Placed[Style[#, 20, Red, Bold], Center] & /@ #1)],
VertexCoordinates -> i], {i, {#2, -#2}}] & @@ ptF[5], Spacer[50]]

Row[Table[Graph[Range[Length@#1], {}, VertexSize -> {.5, .5}, ImageSize -> 300,
VertexLabels -> Thread[Range[Length@#1] ->
(Placed[Style[#, 20, Red, Bold], Center] & /@ #1)],
VertexCoordinates -> i], {i, {Reverse/@#2, -Reverse/@#2}}] & @@ ptF[5], Spacer[50]]
