A208891 Pascal's triangle matrix augmented with a right border of 1's.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 4, 1, 1, 1, 5, 10, 10, 5, 1, 1, 1, 6, 15, 20, 15, 6, 1, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 1, 1, 10, 45, 120, 210, 252, 210, 120, 45

Offset

0,8

Comments

The eigensequence of this triangle starts as 1, 2, 4, 9, 23, 65,... (cf. A007476).

The flattened sequence differs from A135225 only by an additional leading 1.

Links

Table of n, a(n) for n=0..74.

Formula

T(n,n)=1. T(n,k) = A007318(n-1,k) for k<n.

Example

First few rows of the triangle =
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 3, 3, 1, 1;
1, 4, 6, 4, 1, 1;
1, 5, 10, 10, 5, 1, 1;
1, 6, 15, 20, 15, 6, 1, 1;
1, 7, 21, 35, 35, 21, 7, 1, 1;
1, 8, 28, 56, 70, 56, 28, 8, 1, 1;
1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 1;
1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 1;
...

Maple

208891 := proc(n, k)
    if n <0 or k<0 or k>n then
        0;
    elif n = k then
        1 ;
    else
        binomial(n-1, k) ;
    end if;
end proc:
seq(seq(A208891(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Jul 19 2024

Crossrefs

Cf. A007318, A007476

Sequence in context: A124279 A297299 A135225 * A177767 A047030 A047120

Adjacent sequences: A208888 A208889 A208890 * A208892 A208893 A208894

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Mar 03 2012

Status

approved