A147720 Riordan array (1, x(1-x)/(1-3x)).

1, 0, 1, 0, 2, 1, 0, 6, 4, 1, 0, 18, 16, 6, 1, 0, 54, 60, 30, 8, 1, 0, 162, 216, 134, 48, 10, 1, 0, 486, 756, 558, 248, 70, 12, 1, 0, 1458, 2592, 2214, 1168, 410, 96, 14, 1, 0, 4374, 8748, 8478, 5160, 2150, 628, 126, 16

Offset: 0

Author

Paul Barry, Nov 11 2008

Keywords

• easy
• nonn
• tabl

Comments

Array [0,2,1,0,0,0,....] DELTA [1,0,0,0,......] for Deléham DELTA as in A084938.

Row sums are A001835. Diagonal sums are related to A030186.

Row sums of inverse are essentially A091593. A147720*A007318 is A147721.

Examples

			Triangle begins
1;
0,   1;
0,   2,   1;
0,   6,   4,   1;
0,  18,  16,   6,   1;
0,  54,  60,  30,   8,   1;
0, 162, 216, 134,  48,  10,   1;
		

Links

• Indranil Ghosh, Rows 0..100, flattened

Programs

Mathematica

nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1-3*x)/(1-(3+y)*x+y*x^2), {x, 0, nmax}],x],{y,0,nmax}],y]] (* Indranil Ghosh, Mar 10 2017, after Philippe Deléham *)

Formula

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A001835(n), A147722(n), A084120(n) for x = 0, 1, 2, 3 respectively. - Philippe Deléham, Nov 15 2008

G.f.: (1-3*x)/(1-(3+y)*x+y*x^2). - Philippe Deléham, Feb 15 2012