A129687 - OEIS

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A129687

A129686 * A007318.

1, 1, 1, 2, 2, 1, 2, 4, 3, 1, 2, 6, 7, 4, 1, 2, 8, 13, 11, 5, 1, 2, 10, 21, 24, 16, 6, 1, 2, 12, 31, 45, 40, 22, 7, 1, 2, 14, 43, 76, 85, 62, 29, 8, 1, 2, 16, 57, 119, 161, 147, 91, 37, 9, 1, 2, 18, 73, 176, 280, 308, 238, 128, 46, 10, 1, 2, 20, 91, 249, 456

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Row sums = A084215: (1, 2, 5, 10, 20, 40, 80, ...). A007318 * A129686 = A124725.

From Philippe Deléham, Feb 12 2014: (Start)

Riordan array ((1+x^2)/(1-x), x/(1-x)).

Diagonal sums are A000032(n) - 0^n (cf. A000204).

T(n,0) = A046698(n+1).

T(n+1,1) = A004277(n).

T(n+2,2) = A002061(n+1).

T(n+3,3) = A006527(n+1) = A167875(n).

T(n+4,4) = A006007(n+1).

T(n+5,5) = A081282(n+1). (End)

LINKS

Table of n, a(n) for n=0..70.

FORMULA

A129686 * A007318 (Pascal's Triangle), as infinite lower triangular matrices.

T(n,k) = T(n-1,k) + T(n-1,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = T(2,1) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Feb 12 2014

EXAMPLE

First few rows of the triangle:

1, 1;

2, 2, 1;

2, 4, 3, 1;

2, 6, 7, 4, 1;

2, 8, 13, 11, 5, 1;

2, 10, 21, 24, 16, 6, 1;

2, 12, 31, 45, 40, 22, 7, 1;

2, 14, 43, 76, 85, 62, 29, 8, 1;

2, 16, 57, 119, 161, 147, 91, 37, 9, 1;

...