OFFSET
0,5
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
(x+1)(x+3)(x+6)=x^3+10x^2+27x+18, so a(3,j)=1, 10, 27, 18.
The triangle begins:
1
1, 1
1, 4, 3
1, 10, 27, 18
1, 20, 127, 288, 180
1, 35, 427, 2193, 4500, 2700
1, 56, 1162, 11160, 50553, 97200, 56700
MAPLE
for n from 1 to 9 do b[n]:=n*(n+1)/2 od: a[0, 0]:=1:a[1, 0]:=1:a[1, 1]:=1:for i from 2 to 9 do a[i, 0]:=1:for j from 1 to i-1 do a[i, j]:=b[i]*a[i-1, j-1]+ a[i-1, j] od:a[i, i]:=b[i]*a[i-1, i-1] od: seq(seq(a[i, j], j=0..i), i=0..9);
MATHEMATICA
Flatten[Table[Reverse[CoefficientList[Expand[Times@@Table[x+(n(n+1))/2, {n, i}]], x]], {i, 0, 9}]] (* Harvey P. Dale, Nov 11 2011 *)
PROG
(PARI) row(n) = Vec(prod(i=1, n, (x+i*(i+1)/2))); \\ Michel Marcus, Mar 18 2023
CROSSREFS
KEYWORD
AUTHOR
Miklos Kristof, Apr 10 2007
STATUS
approved