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Search: id:A102220
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| A102220 |
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Triangular matrix, read by rows, equal to [2*I - A008459]^(-1), i.e., the matrix inverse of the difference of twice the identity matrix and the triangular matrix of squared binomial coefficients. |
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+0
5
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| 1, 1, 1, 5, 4, 1, 55, 45, 9, 1, 1077, 880, 180, 16, 1, 32951, 26925, 5500, 500, 25, 1, 1451723, 1186236, 242325, 22000, 1125, 36, 1, 87054773, 71134427, 14531391, 1319325, 67375, 2205, 49, 1, 6818444405, 5571505472, 1138150832, 103334336
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column 0 forms A102221. Row sums form twice column 0 for n>0. Matrix logarithm is A102222.
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FORMULA
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T(n, k) = C(n, k)^2*A102221(n-k). T(n, 0) = A102221(n). 2*A102221(n) = Sum_{k=0, n} T(n, k) for n>0.
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EXAMPLE
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Rows begin:
[1],
[1,1],
[5,4,1],
[55,45,9,1],
[1077,880,180,16,1],
[32951,26925,5500,500,25,1],
[1451723,1186236,242325,22000,1125,36,1],...
and equal the term-by-term product of column 0
with the squared binomial coefficients (A008459):
[(1)1^2],
[(1)1^2,(1)1^2],
[(5)1^2,(1)2^2,(1)1^2],
[(55)1^2,(5)3^2,(1)3^2,(1)1^2],
[(1077)1^2,(55)4^2,(5)6^2,(1)4^2,(1)1^2],...
The matrix inverse is [2*I - A008459]:
[1],
[ -1,1],
[ -1,-4,1],
[ -1,-9,-9,1],
[ -1,-16,-36,-16,1],...
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PROGRAM
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(PARI) {T(n, k)=(matrix(n+1, n+1, i, j, if(i==j, 2, 0)-binomial(i-1, j-1)^2)^-1)[n+1, k+1]}
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CROSSREFS
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Cf. A008459, A102221, A102222.
Adjacent sequences: A102217 A102218 A102219 this_sequence A102221 A102222 A102223
Sequence in context: A008955 A152862 A108440 this_sequence A109430 A085917 A102593
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2004
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