A125102 - OEIS

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A125102

Triangle read by rows: T(n,k)=(k+1)binomial(n,k) + [3-(-1)^k]binomial(n,k+1)/2 (0<=k<=n).

1, 2, 2, 3, 6, 3, 4, 12, 10, 4, 5, 20, 22, 18, 5, 6, 30, 40, 50, 26, 6, 7, 42, 65, 110, 81, 38, 7, 8, 56, 98, 210, 196, 140, 50, 8, 9, 72, 140, 364, 406, 392, 204, 66, 9, 10, 90, 192, 588, 756, 924, 624, 306, 82, 10, 11, 110, 255, 900, 1302, 1932, 1590, 1050, 415, 102, 11, 12

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OFFSET

0,2

COMMENTS

Binomial transform of the bidiagonal matrix with (1,2,3...) in the main diagonal and (1,2,1,2,1,2...) in the subdiagonal. Sum of terms in row n = (n+5)*2^(n-1)-2 for n>=1.

LINKS

Table of n, a(n) for n=0..66.

EXAMPLE

First few rows of the triangle are:

2, 2;

3, 6, 3;

4, 12, 10, 4;

5, 20, 22, 18, 5;

6, 30, 40, 50, 26, 6;

7, 42, 65, 110, 81, 38, 7;

...

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