A118980 Triangle read by rows: rows = inverse binomial transforms of columns of A309220.

1, 2, 1, 6, 5, 2, 14, 22, 18, 6, 34, 85, 118, 84, 24, 82, 311, 660, 780, 480, 120, 198, 1100, 3380, 5964, 6024, 3240, 720, 478, 3809, 16380, 40740, 60480, 52920, 25200, 5040, 1154, 13005, 76518, 258804, 531864, 676080, 519840, 221760, 40320, 2786, 43978, 348462, 1564314, 4286880, 7444800, 8240400

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, ...

...

Links

Table of n, a(n) for n=1..52.

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

The leading column is A099425, and the rightmost two diagonals are A038720 and A000142.

Cf. A104509, A117938, A118981, A309220.

Sequence in context: A070918 A113381 A228175 * A351385 A090665 A347952

Adjacent sequences: A118977 A118978 A118979 * A118981 A118982 A118983

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