OFFSET
1,2
COMMENTS
First few columns of A309220:
1, 2, 6, 14, 34, ...
1, 3, 11, 36, 119, ...
1, 4, 18, 76, 322, ...
1, 5, 27, 140, 727, ...
1, 6, 38, 234, 1442, ...
1, 7, 51, 364, 2599, ...
1, 8, 66, 536, 4354, ...
...
EXAMPLE
First few rows of the triangle:
1;
2, 1;
6, 5, 2;
14, 22, 18, 6;
34, 85, 118, 84, 24;
82, 311, 660, 780, 480, 120;
...
Column 3 of A309220 = (6, 11, 18, 27, 38, 51, ...), whose inverse binomial transform is (6, 5, 2).
MAPLE
with(transforms);
M := 12;
T := [1];
S := series((1 + x^2)/(1-x-x^2 + x*y), x, 120):
for n from 1 to M do
R2 := expand(coeff(S, x, n));
R3 := [seq(abs(coeff(R2, y, n-i)), i=0..n)];
f := k-> add( R3[i]*k^(n-i+1), i=1..nops(R3) ):
s1 := [seq(f(i), i=1..3*n)];
s2 := BINOMIALi(s1);
s3 := [seq(s2[i], i=1..n+1)];
T := [op(T), op(s3)];
od:
T; # N. J. A. Sloane, Aug 12 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 07 2006
EXTENSIONS
Edited and extended by N. J. A. Sloane, Aug 12 2019, guided by the comments of R. J. Mathar from Oct 30 2011
STATUS
approved