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A110814
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Inverse of a triangle of pyramidal numbers.
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1
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1, -3, 1, 7, -4, 1, -15, 11, -5, 1, 31, -26, 16, -6, 1, -63, 57, -42, 22, -7, 1, 127, -120, 99, -64, 29, -8, 1, -255, 247, -219, 163, -93, 37, -9, 1, 511, -502, 466, -382, 256, -130, 46, -10, 1, -1023, 1013, -968, 848, -638, 386, -176, 56, -11, 1, 2047, -2036, 1981, -1816, 1486, -1024, 562, -232, 67, -12, 1, -4095, 4083
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Inverse of A110813. Array factors as (1/(1+2x),x)*(1/(1+x),x/(1+x)). Row sums are (-2)^n. Diagonal sums are (-1)^n*A008466(n+2). Signed version of A104709.
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FORMULA
| Number triangle T(n, k)=sum{j=0..n, (-2)^(n-j)*binomial(j, k)*(-1)^(j-k)}; Riordan array (1/(1+3x+2x^2), x/(1+x)).
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EXAMPLE
| Rows begin
1,
-3,1;
7,-4,1;
-15,11,-5,1;
31,-26,16,-6,1;
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MAPLE
| A110814_row := proc(n) add((-1)^k*add(binomial(n, n-i)*x^(n-k-1), i=0..k), k=0..n-1); coeffs(sort(%)) end; seq(print(A110814_row(n)), n=1..6); # Peter Luschny, Sep 29 2011
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CROSSREFS
| Sequence in context: A013602 A086272 A104709 * A193970 A158841 A021319
Adjacent sequences: A110811 A110812 A110813 * A110815 A110816 A110817
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 05 2005
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