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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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..47.

EXAMPLE

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; ...

PROG

(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)))}

CROSSREFS

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

Sequence in context: A051292 A094424 A265241 * A083677 A075803 A127966

Adjacent sequences:  A166885 A166886 A166887 * A166889 A166890 A166891

KEYWORD

nonn,tabf

AUTHOR

Paul D. Hanna, Nov 22 2009

STATUS

approved

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Last modified August 7 08:55 EDT 2020. Contains 336274 sequences. (Running on oeis4.)