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Search: id:A102610
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| A102610 |
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Triangle read by rows: coefficients of characteristic polynomials of lower triangular matrix of Robbins triangle numbers. |
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+0
1
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| 1, -1, 1, -2, 1, 1, -4, 5, -2, 1, -11, 33, -37, 14, 1, -53, 495, -1423, 1568, -588, 1, -482, 23232, -213778, 612035, -673260, 252252, 1, -7918, 3607384, -172966930, 1590265243, -4551765520, 5006613612, -1875745872, 1, -226266, 1732486848, -787838048562, 37768573496883, -347235787044084
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Roots of n-th characteristic polynomial are the first n Robbins numbers (A005130). Second column of triangle is partial sums of Robbins numbers.)
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EXAMPLE
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Generation of the triangle:
We begin with A048601
1
1 1
2 3 2
7 14 14 7
42 105 135 105 42
...
and get polynomials
x - 1
x^2 - 2*x + 1
x^3 - 4*x^2 + 5*x - 2
x^4 - 11*x^3 + 33*x^2 - 37*x + 14
x^5 - 53*x^4 + 495*x^3 - 1423*x^2 + 1568*x - 588
...
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PROGRAM
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(PARI) T(n, k) = binomial(n+k-2, k-1)*((2*n-k-1)!/(n-k)!)*prod(j=0, n-2, ((3*j+1)!/(n+j)!)) RM(n)=M=matrix(n, n); for(l=1, n, for(k=1, l, M[l, k]=T(l, k))); M for(i=1, 10, print(charpoly(RM(i))))
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CROSSREFS
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Cf. A005130, A048601.
Sequence in context: A158471 A158472 A118686 this_sequence A134172 A078047 A143392
Adjacent sequences: A102607 A102608 A102609 this_sequence A102611 A102612 A102613
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KEYWORD
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sign,tabl
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AUTHOR
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Lambert Klasen (lambert.klasen(AT)gmx.net) and Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 30 2005
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