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A097807
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Riordan array (1/(1+x),1) read by rows.
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11
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1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Columns have g.f. x^k/(1+x).
Row sums are A059841. Diagonal sums are (-1)^n*A008619 with g.f. 1/((1+x)(1-x^2)).
Inverse of A097806. Equals B^(-1)*A097805, where B is the binomial matrix.
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LINKS
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Table of n, a(n) for n=0..80.
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FORMULA
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Triangle array of numbers T(n, k) with T(n, k)=if(n>=k, (-1)^(n-k), 0).
T(n+1,0) = -T(n,0), T(n+1,k+1) = T(n,k) for k = 1..n. - Reinhard Zumkeller, Sep 17 2014
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EXAMPLE
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Rows begin
1;
-1,1;
1,-1,1;
-1,1,-1,1;
1,-1,1,-1,1;
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MATHEMATICA
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(* The function RiordanArray is defined in A256893. *)
rows = 12;
R = RiordanArray[1/(1 + #)&, #&, rows];
R // Flatten (* Jean-François Alcover, Jul 20 2019 *)
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PROG
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(Haskell)
a097807 n k = a097807_tabl !! n !! k
a097807_row n = a097807_tabl !! n
a097807_tabl = iterate(\xs@(x:_) -> - x : xs) [1]
-- Reinhard Zumkeller, Sep 17 2014
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CROSSREFS
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Cf. A008619, A059841, A097805, A097806.
Sequence in context: A244513 A020985 A034947 * A014077 A174351 A181432
Adjacent sequences: A097804 A097805 A097806 * A097808 A097809 A097810
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry, Aug 25 2004
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STATUS
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approved
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