A038255 Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j).

1, 6, 1, 36, 12, 1, 216, 108, 18, 1, 1296, 864, 216, 24, 1, 7776, 6480, 2160, 360, 30, 1, 46656, 46656, 19440, 4320, 540, 36, 1, 279936, 326592, 163296, 45360, 7560, 756, 42, 1, 1679616, 2239488, 1306368, 435456, 90720, 12096, 1008

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• easy

Comments

T(n,k) = A013613(n,n-k), 0 <= k <= n. - Reinhard Zumkeller, Nov 21 2013

Examples

			1
6, 1
36, 12, 1
216, 108, 18, 1
1296, 864, 216, 24, 1
7776, 6480, 2160, 360, 30, 1
46656, 46656, 19440, 4320, 540, 36, 1
279936, 326592, 163296, 45360, 7560, 756, 42, 1
1679616, 2239488, 1306368, 435456, 90720, 12096, 1008, 48, 1
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
• Naiomi T. Cameron and Asamoah Nkwanta, On Some (Pseudo) Involutions in the Riordan Group, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.7.
• B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.

Crossrefs

Cf. A038207.

Cf. A000420 (row sums), A013613 (mirrored), A110440, A007318, A000400.

Programs

Haskell

a038255 n k = a038255_tabl !! n !! k
a038255_row n = a038255_tabl !! n
a038255_tabl = map reverse a013613_tabl
-- Reinhard Zumkeller, Nov 21 2013

Maple

for i from 0 to 8 do seq(binomial(i, j)*6^(i-j), j = 0 .. i) od; # Zerinvary Lajos, Dec 21 2007

Mathematica

Table[Binomial[n,m]6^(n-m),{n,0,10},{m,0,n}]//Flatten (* Harvey P. Dale, Dec 25 2019 *)

Formula

G.f.: 1/(1 - 6*x - x*y). - Ilya Gutkovskiy, Apr 21 2017