A147724 a(n) = C(3,n) DELTA C(0,n).

1, 1, 1, 4, 5, 1, 25, 33, 9, 1, 172, 238, 78, 13, 1, 1201, 1745, 667, 139, 17, 1, 8404, 12807, 5583, 1376, 216, 21, 1, 58825, 93841, 45822, 12950, 2429, 309, 25, 1, 411772, 686288, 370108, 117458, 25366, 3890, 418, 29, 1, 2882401, 5009889, 2951034, 1035834, 251583, 44607, 5823, 543, 33, 1

Offset: 0

Author

Paul Barry, Nov 11 2008

Keywords

• easy
• nonn
• tabl

Comments

Triangle [1,3,3,1,0,0,0,...] DELTA [1,0,0,0,...] with Deléham DELTA as in A084938.

First column is A034494(n-1). Row sums are A147725. A147724 = A147723*A007318.

Examples

			Triangle begins
    1;
    1,   1;
    4,   5,   1;
   25,  33,   9,   1;
  172, 238,  78,  13,   1;
		

Links

• Indranil Ghosh, Rows 0..100, flattened

Crossrefs

Cf. A147721.

Programs

Mathematica

nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 7*x + 3*x^2)/(1 - 8*x + 7*x^2 - x*y + 4*x^2*y) , {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 10 2017 *)

Formula

Riordan array ((1-7*x+3*x^2)/(1-8*x+7*x^2), x*(1-4*x)/(1-8*x+7*x^2)).

G.f.: (1 - 7*x + 3*x^2)/(1 - 8*x + 7*x^2 - x*y + 4*x^2*y). - Philippe Deléham, Oct 29 2013

T(n,k) = 8*T(n-1,k) + T(n-1,k-1) - 7*T(n-2,k) - 4*T(n-2,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 4, T(2,1) = 5, T(n,k) = 0 if k > n or if k < 0. - Philippe Deléham, Oct 29 2013