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

0,4

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.

Links

Indranil Ghosh, Rows 0..100, flattened

Formula

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

Example

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

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 *)

Crossrefs

Cf. A147721.

Sequence in context: A283263 A109962 A102230 * A110519 A286796 A286718

Adjacent sequences: A147721 A147722 A147723 * A147725 A147726 A147727

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 11 2008

Status

approved