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Triangle of coefficients in expansion of (2+3x)^n.
8

%I #26 Apr 22 2014 03:04:08

%S 1,2,3,4,12,9,8,36,54,27,16,96,216,216,81,32,240,720,1080,810,243,64,

%T 576,2160,4320,4860,2916,729,128,1344,6048,15120,22680,20412,10206,

%U 2187,256,3072,16128,48384,90720,108864,81648,34992,6561,512

%N Triangle of coefficients in expansion of (2+3x)^n.

%C Row sums give A000351; central terms give A119309. - _Reinhard Zumkeller_, May 14 2006

%H Reinhard Zumkeller, <a href="/A013620/b013620.txt">Rows n = 0..125 of triangle, flattened</a>

%H Gábor Kallós, <a href="http://dx.doi.org/10.5802/ambp.211">A generalization of Pascal’s triangle using powers of base numbers</a>, Annales mathématiques Blaise Pascal, 13 no. 1 (2006), p. 1-15.

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%F G.f.: 1 / [1 - x(2+3y)].

%F T(n,k) = A007318(n,k) * A036561(n,k). - _Reinhard Zumkeller_, May 14 2006

%e Triangle begins:

%e 1;

%e 2,3;

%e 4,12,9;

%e 8,36,54,27;

%e 16,96,216,216,81;

%t Flatten[Table[Binomial[i, j] 2^(i-j) 3^j, {i, 0, 10}, {j, 0, i}]] (* _Vincenzo Librandi_, Apr 22 2014 *)

%o (Haskell)

%o a013620 n k = a013620_tabl !! n !! k

%o a013620_row n = a013620_tabl !! n

%o a013620_tabl = iterate (\row ->

%o zipWith (+) (map (* 2) (row ++ [0])) (map (* 3) ([0] ++ row))) [1]

%o -- _Reinhard Zumkeller_, May 26 2013, Apr 02 2011

%Y Cf. A038220, A000079, A000244, A013613.

%K tabl,nonn,easy

%O 0,2

%A _N. J. A. Sloane_.