OFFSET
1,2
COMMENTS
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
EXAMPLE
Triangle begins:
1;
2, 2;
7, 2, 3;
10, 10, 3, 4;
23, 12, 11, 4, 5;
36, 30, 17, 14, 5, 6;
MAPLE
p:= (f, g)-> zip((x, y)-> x+y, f, g, 0):
b:= proc(n, i) option remember; local f, g;
if n=0 then [1]
elif i=1 then [1, n]
else f:= b(n, i-1); g:= `if`(i>n, [0], b(n-i, i));
p (p (f, g), [0$i, g[1]])
fi
end:
T:= proc(n) local l;
l:= b(n, n);
seq (add (l[i+2*j+1]*(i+2*j), j=0..(n-i)/2), i=1..n)
end:
seq (T(n), n=1..14); # Alois P. Heinz, Mar 21 2012
MATHEMATICA
p[f_, g_] := With[{m = Max[Length[f], Length[g]]}, PadRight[f, m, 0] + PadRight[g, m, 0]]; b[n_, i_] := b[n, i] = Module[{f, g}, Which[n == 0, {1}, i == 1, {1, n}, True, f = b[n, i-1]; g = If[i>n, {0}, b[n-i, i]]; p[p[f, g], Append[Array[0&, i], g[[1]]]]]]; T[n_] := Module[{l}, l = b[n, n]; Table[Sum[l[[i+2j+1]]*(i+2j), {j, 0, (n-i)/2}], {i, 1, n}]]; Table[T[n], {n, 1, 14}] // Flatten (* Jean-François Alcover, Mar 11 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Feb 28 2012
EXTENSIONS
More terms from Alois P. Heinz, Mar 21 2012
STATUS
approved