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EXAMPLE
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Triangle begins:
1;
1;
1, 1;
1, 4, 2, 2;
1, 10, 22, 22, 18, 13, 12;
1, 20, 112, 232, 382, 348, 456, 390, 420, 334, 286;
...
The transposed triangle, as given by Nelson, begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 4, 10, 20, 35, 56, 84, ...
2, 22, 112, 392, 1092, 2604, ...
2, 22, 232, 1744, 9220, 37444, ...
18, 382, 4474, 40414, 280214, ...
13, 348, 8435, 123704, 1321879, ...
12, 456, 12732, 276324, 4578596, ...
390, 17337, 550932, 12512827, ...
420, 21158, 917884, 29499764, ...
334, 27853, 1510834, 62132126, ...
286, 33940, 2166460, 120837274, ...
41230, 3370312, 221484557, ...
45048, 4810150, 393364848, ...
50752, 7264302, 666955139, ...
41826, 10435954, 1134705692, ...
33592, 15227802, 1933708535, ...
...
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MAPLE
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s:= proc(n) s(n):=`if`(n=0, [], [s(n-1), []]) end:
f:= l-> l=[] or l[1]=[] and f(l[2]):
v:= proc(l) v(l):=`if`(f(l), [], [`if`(l[1]<>[],
[l[1][1], [l[1][2], l[2]]], [][]),
seq([w, l[2]], w=v(l[1])), seq([l[1], w], w=v(l[2]))])
end:
p:= proc(l) p(l):=`if`(f(l), 1, add(expand(x*p(w)), w=v(l))) end:
T:= n-> (h-> seq(coeff(h, x, i), i=ldegree(h)..degree(h)))(p(s(n))):
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