OFFSET
1,2
COMMENTS
Row n lists the partial sums of row n of triangle A138785.
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
FORMULA
T(n,k) = sum_{j=1..k} A138785(n,j).
EXAMPLE
Triangle begins:
1;
2, 4;
4, 6, 9;
7, 13, 16, 20;
12, 20, 26, 30, 35;
19, 35, 47, 55, 60, 66;
30, 52, 70, 82, 92, 98, 105;
45, 83, 110, 134, 149, 161, 168, 176;
67, 119, 164, 196, 221, 239, 253, 261, 270;
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]*i])
fi
end:
T:= proc(n, k) option remember;
b(n, n)[k+1] +`if`(k<2, 0, T(n, k-1))
end:
seq (seq (T(n, k), k=1..n), n=1..12); # Alois P. Heinz, May 02 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], i*g[[1]]]]]]; T[n_, k_] := T[n, k] = b[n, n][[k+1]] + If[k<2, 0, T[n, k-1]]; Table[Table[T[n, k], {k, 1, n}], {n, 1, 12 }] // Flatten (* Jean-François Alcover, Mar 11 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, May 01 2012
STATUS
approved