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

Author

Gary W. Adamson, Mar 03 2012

Keywords

• nonn
• easy
• tabl

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.

Examples

			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;
...
		

Crossrefs

Cf. A007318, A007476

Programs

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

Formula

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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