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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

Table of n, a(n) for n=0..54.

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.

Cf. A057728, A152568, A152570, A152571.

Sequence in context: A157212 A156600 A329118 * A203346 A176793 A118190

Adjacent sequences:  A152569 A152570 A152571 * A152573 A152574 A152575

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 May 25 17:36 EDT 2020. Contains 334595 sequences. (Running on oeis4.)