A147721 a(n) = C(2,n) DELTA C(0,n).

1, 1, 1, 3, 4, 1, 11, 17, 7, 1, 41, 72, 40, 10, 1, 153, 301, 208, 72, 13, 1, 571, 1244, 1021, 446, 113, 16, 1, 2131, 5093, 4819, 2525, 813, 163, 19, 1, 7953, 20688, 22104, 13452, 5218, 1336, 222, 22, 1, 29681, 83481, 99192, 68568, 30986, 9586, 2042, 290, 25, 1

Offset: 0

Author

Paul Barry, Nov 11 2008

Keywords

• easy
• nonn
• tabl

Comments

Triangle T equal to [1,2,1,0,0,0,...] DELTA [1,0,0,0,...] for Deléham DELTA as in A084938.

T = A147720*A007318. Row sums are A147722.

Examples

			Triangle begins
    1;
    1,   1;
    3,   4,   1;
   11,  17,   7,   1;
   41,  72,  40,  10,   1;
  153, 301, 208,  72,  13,   1;
		

Links

• Indranil Ghosh, Rows 0..100, flattened

Crossrefs

Cf. A129267, A007318, A147703.

Programs

Mathematica

nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 3*x)/(1 - 4*x + (1 + y)*x^2 - y*x), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 10 2017, after Philippe Deléham *)

Formula

Riordan array ((1-3x)/(1-4x+x^2), x(1-x)/(1-4x+x^2)).

T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n > 1. - Philippe Deléham, Feb 13 2012

G.f.: (1-3*x)/(1-4*x+(1+y)*x^2-y*x). - Philippe Deléham, Feb 13 2012

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A001835(n), A147722(n), A084120(n) for x = -1, 0, 1, 2 respectively. - Philippe Deléham, Feb 13 2012