A013620 Triangle of coefficients in expansion of (2+3x)^n.

1, 2, 3, 4, 12, 9, 8, 36, 54, 27, 16, 96, 216, 216, 81, 32, 240, 720, 1080, 810, 243, 64, 576, 2160, 4320, 4860, 2916, 729, 128, 1344, 6048, 15120, 22680, 20412, 10206, 2187, 256, 3072, 16128, 48384, 90720, 108864, 81648, 34992, 6561, 512

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Comments

Row sums give A000351; central terms give A119309. - Reinhard Zumkeller, May 14 2006

Examples

			Triangle begins:
1;
2,3;
4,12,9;
8,36,54,27;
16,96,216,216,81;
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
• Gábor Kallós, A generalization of Pascal’s triangle using powers of base numbers, Annales mathématiques Blaise Pascal, 13 no. 1 (2006), p. 1-15.
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A038220, A000079, A000244, A013613.

Programs

Haskell

a013620 n k = a013620_tabl !! n !! k
a013620_row n = a013620_tabl !! n
a013620_tabl = iterate (\row ->
   zipWith (+) (map (* 2) (row ++ [0])) (map (* 3) ([0] ++ row))) [1]
-- Reinhard Zumkeller, May 26 2013, Apr 02 2011

Mathematica

Flatten[Table[Binomial[i, j] 2^(i-j) 3^j, {i, 0, 10}, {j, 0, i}]] (* Vincenzo Librandi, Apr 22 2014 *)

Formula

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

T(n,k) = A007318(n,k) * A036561(n,k). - Reinhard Zumkeller, May 14 2006