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A152572
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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
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3
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-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)
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OFFSET
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0,4
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LINKS
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FORMULA
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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)
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EXAMPLE
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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;
...
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MATHEMATICA
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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}]]
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PROG
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(Maxima)
T(n, k) := if k = n then -1 else if k = 0 then 5^(n - 1) else -5^(n - k - 1);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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