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A147724 a(n) = C(3,n) DELTA C(0,n). 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)