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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 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.)