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A152572 Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 5^(n - 1), T(n,k) = -5^(n - k - 1), 1 <= k <= n - 1 3
-1, 1, -1, 5, -1, -1, 25, -5, -1, -1, 125, -25, -5, -1, -1, 625, -125, -25, -5, -1, -1, 3125, -625, -125, -25, -5, -1, -1, 15625, -3125, -625, -125, -25, -5, -1, -1, 78125, -15625, -3125, -625, -125, -25, -5, -1, -1, 390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
From Franck Maminirina Ramaharo, Jan 08 2019: (Start)
G.f.: -(1 - 6*y + 2*x*y^2)/(1 - (5 + x)*y + 5*x*y^2).
E.g.f.: -(10 - 2*x - (5 - 2*x)*exp(5*y) + (20 - 5*x)*exp(x*y))/(25 - 5*x). (End)
EXAMPLE
Triangle begins:
-1;
1, -1;
5, -1, -1;
25, -5, -1, -1;
125, -25, -5, -1, -1;
625, -125, -25, -5, -1, -1;
3125, -625, -125, -25, -5, -1, -1;
15625, -3125, -625, -125, -25, -5, -1, -1;
78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
1953125, -390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
...
MATHEMATICA
b[0] = {-1}; b[1] = {1, -1};
b[n_] := b[n] = Join[{5^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];
Flatten[Table[b[n], {n, 0, 10}]]
PROG
(Maxima)
T(n, k) := if k = n then -1 else if k = 0 then 5^(n - 1) else -5^(n - k - 1);
create_list(T(n, k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Jan 08 2019 */
CROSSREFS
Row sums (except row 0): A125833.
Sequence in context: A157212 A156600 A329118 * A203346 A176793 A118190
KEYWORD
sign,easy,tabl
AUTHOR
Roger L. Bagula, Dec 08 2008
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 08 2019
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)