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A113313
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Riordan array (1-2x,x/(1-x)).
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1
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1, -2, 1, 0, -1, 1, 0, -1, 0, 1, 0, -1, -1, 1, 1, 0, -1, -2, 0, 2, 1, 0, -1, -3, -2, 2, 3, 1, 0, -1, -4, -5, 0, 5, 4, 1, 0, -1, -5, -9, -5, 5, 9, 5, 1, 0, -1, -6, -14, -14, 0, 14, 14, 6, 1, 0, -1, -7, -20, -28, -14, 14, 28, 20, 7, 1, 0, -1, -8, -27, -48, -42, 0, 42, 48, 27, 8, 1, 0, -1, -9, -35
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OFFSET
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0,2
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COMMENTS
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Row sums are (1,-1,0,0,0,...) = 2*C(0,n) - C(1,n).
Diagonal sums are -2*0^n - F(n-4) with g.f. (1 - 3x + 2x^2) / (1 - x - x^2).
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LINKS
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FORMULA
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T(n, k) = C(n-1, n-k) - 2*C(n-2, n-k-1).
exp(x) * e.g.f. for row n = e.g.f. for diagonal n. For example, for n = 3 we have exp(x)*(-x + x^3/3!) = -x - 2*x^2/2! - 2*x^3/3! + 5*x^5/5! + .... The same property holds more generally for Riordan arrays of the form ( f(x), x/(1 - x) ). - Peter Bala, Dec 21 2014
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EXAMPLE
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The triangle T(n, k) begins:
n\k 0 1 2 3 4 5 6 7 8 9 10 ...
0: 1
1: -2 1
2: 0 -1 1
3: 0 -1 0 1
4: 0 -1 -1 1 1
5: 0 -1 -2 0 2 1
6: 0 -1 -3 -2 2 3 1
7: 0 -1 -4 -5 0 5 4 1
8: 0 -1 -5 -9 -5 5 9 5 1
9: 0 -1 -6 -14 -14 0 14 14 6 1
10: 0 -1 -7 -20 -28 -14 14 28 20 7 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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