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Search: id:A103450
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| A103450 |
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A figurate number triangle read by rows. |
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+0
1
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| 1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 12, 7, 1, 1, 9, 22, 22, 9, 1, 1, 11, 35, 50, 35, 11, 1, 1, 13, 51, 95, 95, 51, 13, 1, 1, 15, 70, 161, 210, 161, 70, 15, 1, 1, 17, 92, 252, 406, 406, 252, 92, 17, 1, 1, 19, 117, 372, 714, 882, 714, 372, 117, 19, 1, 1, 21, 145, 525, 1170, 1722
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row coefficients are the absolute values of the coefficients of the characteristic polynomials of the n X n matrices A(n) with A(n)_i,i=2, i>0, A(n)_i,j=1, otherwise (starts with (0,0) position).
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FORMULA
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Number triangle T(n, k)=if(k<=n, if(k=0, 1, binomial(n-k, k-1)((k+1)(n-k)+k)/k, 0), 0); T(n, 0)=1, T(0, k)=0, k>0, T(n, k)=T(n-1, k-1)+T(n-1, k)+binomial(n-2, k-1); Column k is generated by (1+kx)x^k/(1-x)^(k+1); Rows are coefficients of the polynomials P(0, x)=1, P(n, x)=(1+x)^(n-2)(1+(n+1)x+x^2), n>0
T(n,k)=sum{j=0..n, C(k,k-j)*C(n-k,j)*(j+1)}*[k<=n]; - Paul Barry (pbarry(AT)wit.ie), Oct 28 2006
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EXAMPLE
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Rows begin {1}, {1,1}, {1,3,1}, {1,5,5,1}, {1,7,12,7,1},...
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CROSSREFS
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Row sums are A045623. Columns include A005408, A000326, A002412, A002418.
Sequence in context: A026681 A109128 A113245 this_sequence A128254 A026714 A008288
Adjacent sequences: A103447 A103448 A103449 this_sequence A103451 A103452 A103453
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 06 2005
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