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A179430 Triangular matrix T where column 0 of T^m equals C(m*3^(n-1), n) at row n for n>=0, m>=0. 4
1, 1, 1, 3, 9, 1, 84, 405, 81, 1, 17550, 121500, 32805, 729, 1, 25621596, 247203171, 82255257, 2539107, 6561, 1, 268715232324, 3543210805275, 1382411964132, 53628242751, 199290375, 59049, 1, 21091830512086620, 373203783345533355 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

EXAMPLE

Triangle T begins:

1;

1, 1;

3, 9, 1;

84, 405, 81, 1;

17550, 121500, 32805, 729, 1;

25621596, 247203171, 82255257, 2539107, 6561, 1;

268715232324, 3543210805275, 1382411964132, 53628242751, 199290375, 59049, 1;

21091830512086620, 373203783345533355, 165018275857291311, 7607829219099993, 36456526295226, 15884240049, 531441, 1; ...

where column 0 of T equals A179431(n) = C(3^(n-1), n):

[1, 1, 3, 84, 17550, 25621596, 268715232324, ...]. ...

Illustrate row n in column 0 of T^m equals C(m*3^(n-1), n) as follows.

Matrix square T^2 begins:

1;

2, 1;

15, 18, 1;

816, 1539, 162, 1;

316251, 833490, 124659, 1458, 1;

873642672, 3060203490, 585411786, 9861183, 13122, 1; ...

where column 0 of T^2 equals A179432(n) = C(2*3^(n-1), n):

[1, 2, 15, 816, 316251, 873642672, 17743125256857, ...]. ...

Matrix cube T^3 begins:

1;

3, 1;

36, 27, 1;

2925, 3402, 243, 1;

1663740, 2667411, 275562, 2187, 1;

6774333588, 14164214850, 1896890076, 21966228, 19683, 1; ...

where column 0 of T^3 equals A136393(n) = C(3^n, n):

[1, 3, 36, 2925, 1663740, 6774333588, 204208594169580, ...].

PROG

(PARI) {T(n, k)=local(M=matrix(n+1, n+1, r, c, binomial(r*3^(c-2), c-1)), P); P=matrix(n+1, n+1, r, c, binomial((r+1)*3^(c-2), c-1)); (P~*M~^-1)[n+1, k+1]}

CROSSREFS

Cf. A179431, A179432, A136393, A179433, A179434, variant: A136467.

Sequence in context: A128733 A128724 A128753 * A016048 A256501 A229099

Adjacent sequences:  A179427 A179428 A179429 * A179431 A179432 A179433

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 20 2010

STATUS

approved

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)