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A208058 Triangle by rows relating to the factorials, generated from A002260. 3
1, 1, 1, 1, 2, 1, 2, 4, 3, 1, 6, 12, 9, 4, 1, 24, 48, 36, 16, 5, 1, 120, 240, 180, 80, 25, 6, 1, 720, 1440, 1080, 480, 150, 36, 7, 1, 5040, 10080, 7560, 3360, 1050, 252, 49, 8, 1, 40320, 80640, 60480, 26880, 8400, 2016, 392, 64, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums = A054091: (1, 2, 4, 10, 32, 130, 652,...)
Left border = the factorials, A000142 prefaced with a 1.
LINKS
FORMULA
Inverse of:
1;
-1, 1;
1, -2, 1;
-1, 2, -3, 1;
1, -2, 3, -4, 1;
..., where triangle A002260 = (1; 1,2; 1,2,3;...)
EXAMPLE
First few rows of the triangle =
1;
1, 1;
1, 2, 1;
2, 4, 3, 1;
6, 12, 9, 4, 1;
24, 48, 36, 16, 5, 1;
120, 240, 180, 80, 25, 6, 1;
720, 1440, 1080, 480, 150, 36, 7, 1;
5040, 10080, 7560, 3360, 1050, 252, 49, 8, 1;
...
MAPLE
T:= proc(n) option remember; local M, k;
M:= Matrix(n+1, (i, j)->
`if`(i=j, 1, `if`(i>j, j*(-1)^(i+j), 0)))^(-1);
seq(M[n+1, k], k=1..n+1)
end:
seq(T(n), n=0..14); # Alois P. Heinz, Feb 24 2012
MATHEMATICA
T[n_] := T[n] = Module[{M}, M = Table[If[i == j, 1, If[i>j, j*(-1)^(i+j), 0]], {i, 1, n+1}, {j, 1, n+1}] // Inverse; M[[n+1]]]; Table[T[n], {n, 0, 14}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A179750 A091173 A101897 * A078142 A133422 A331136
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Feb 22 2012
STATUS
approved

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)