A166888 Triangle T(n,k), read by rows n>=0 with terms k=1..3^n, where row n lists the coefficients in the n-th iteration of x*(1+x)^2.

1, 1, 2, 1, 1, 4, 10, 18, 23, 22, 15, 6, 1, 1, 6, 27, 102, 333, 960, 2472, 5748, 12150, 23388, 40926, 64872, 92772, 119216, 137112, 140526, 127677, 102150, 71331, 42954, 21939, 9288, 3156, 822, 153, 18, 1, 1, 8, 52, 300, 1578, 7692, 35094, 150978

Offset: 0

Author

Paul D. Hanna, Nov 22 2009

Keywords

• nonn
• tabf

Examples

			Triangle begins:
1;
1,2,1;
1,4,10,18,23,22,15,6,1;
1,6,27,102,333,960,2472,5748,12150,23388,40926,64872,92772,...;
1,8,52,300,1578,7692,35094,150978,615939,2393628,8892054,...;
1,10,85,660,4790,32920,215988,1360638,8265613,48585702,...;
1,12,126,1230,11385,101010,864813,7178700,57976074,456783888,...;
1,14,175,2058,23163,251832,2660028,27405798,276215313,...;
1,16,232,3192,42308,544600,6842220,84191772,1017153322,...;
1,18,297,4680,71388,1061712,15463512,221228244,3115739358,...;
1,20,370,6570,113355,1912590,31683051,516686346,8311401351,...;
1,22,451,8910,171545,3237520,60108576,1100544720,19906483168,...;
1,24,540,11748,249678,5211492,107184066,2176952910,43733857365,...;
...
The initial diagonals in this triangle begin:
A154256 = [1,2,10,102,1578,32920,864813,27405798,1017153322,...];
A119820 = [1,4,27,300,4790,101010,2660028,84191772,3115739358,...];
A166889 = [1,6,52,660,11385,251832,6842220,221228244,8311401351,...].
The diagonals are transformed one into the other by
triangle A166890, which begins:
1;
2,1;
9,4,1;
78,30,6,1;
1038,364,63,8,1;
18968,6233,986,108,10,1;
443595,139008,20685,2072,165,12,1;
12681960,3833052,545736,51494,3750,234,14,1; ...
		

Crossrefs

Cf. diagonals: A154256, A119820, A166889, variants: A166880, A122888.

Programs

PARI

{T(n, k)=local(F=x+2*x^2+x^3, G=x+x*O(x^k)); if(n<0, 0, for(i=1, n, G=subst(F, x, G)); return(polcoeff(G, k, x)))}