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Search: id:A045912
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| A045912 |
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Triangle of coefficients of characteristic polynomial of negative Pascal matrix with (i,j)-th entry -C(i+j-2,i-1). |
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4
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| 1, 1, 1, 1, 3, 1, 1, 9, 9, 1, 1, 29, 72, 29, 1, 1, 99, 626, 626, 99, 1, 1, 351, 6084, 13869, 6084, 351, 1, 1, 1275, 64974, 347020, 347020, 64974, 1275, 1, 1, 4707, 744193, 9952274, 21537270, 9952274, 744193, 4707, 1, 1, 17577, 8965323
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Sum of k-th row is A006366(n). Columns give A006134, A006135, A006136.
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REFERENCES
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W. F. Lunnon "The Pascal matrix", Fib. Quart. vol. 15 (1977) pp. 201-204.
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LINKS
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P. Di Francesco, P. Zinn-Justin and J.-B. Zuber, Determinant formulae for some tiling problems...
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EXAMPLE
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1; 1,1; 1,3,1; 1,9,9,1; 1,29,72,29,1; ...
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PROGRAM
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(PARI) T(n, k)=if(n<0, 0, (-1)^(n+k)*polcoeff(charpoly(matrix(n, n, i, j, binomial(i+j-2, i-1))), k))
(PARI) T(n, k)=if(n<0, 0, polcoeff(charpoly(-matrix(n, n, i, j, binomial(i+j-2, i-1))), k))
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CROSSREFS
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Sequence in context: A050153 A106340 A118180 this_sequence A106268 A060543 A060540
Adjacent sequences: A045909 A045910 A045911 this_sequence A045913 A045914 A045915
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KEYWORD
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nonn
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AUTHOR
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Fred Lunnon (fred(AT)csa5.cs.may.ie)
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