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Search: id:A070918
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| A070918 |
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Triangle of coefficients of polynomials with first n prime numbers as roots. |
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1
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| -2, 1, 6, -5, 1, -30, 31, -10, 1, 210, -247, 101, -17, 1, -2310, 2927, -1358, 288, -28, 1, 30030, -40361, 20581, -5102, 652, -41, 1, -510510, 716167, -390238, 107315, -16186, 1349, -58, 1, 9699690, -14117683, 8130689, -2429223, 414849, -41817, 2451, -77, 1, -223092870, 334406399, -201123530
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Analogue of the Stirling numbers of the first kind (A008275): The Stirling numbers (beginning with the 2nd row) are the coefficients of the polynomials having exactly the first n natural numbers as roots. This sequence (beginning with first row) consists of the coefficients of the polynomials having exactly the first n prime numbers as roots.
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EXAMPLE
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Row 4 of this sequence is 210, -247, 101, -17, 1 because (x-prime(1))(x-prime(2))(x-prime(3))(x-prime(4)) = (x-2)(x-3)(x-5)(x-7) = x^4 - 17*x^3 + 101*x^2 - 247*x + 210.
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PROGRAM
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(PARI) p=1; for(k=1, 10, p=p*(x-prime(k)); for(n=0, k, print1(polcoeff(p, n), ", ")))
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CROSSREFS
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Cf. A008275 (Stirling numbers of first kind).
Sequence in context: A049444 A136124 A143491 this_sequence A113381 A118980 A090665
Adjacent sequences: A070915 A070916 A070917 this_sequence A070919 A070920 A070921
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KEYWORD
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sign,tabl
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 20 2002
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