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Search: id:A113532
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| A113532 |
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1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6. |
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+0
2
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| 1, 28, 769, 7108, 36409, 131836, 380713, 937924, 2054353, 4110364, 7654321, 13446148, 22505929, 36167548, 56137369, 84557956, 124076833, 177920284, 249972193, 344857924, 468033241, 625878268, 825796489, 1076318788
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OFFSET
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0,2
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COMMENT
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1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7*n^6 is the derivative of 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 = (x^8 - 1)/(x-1). a(2) = 1 + 2*2 + 3*2^2 + 4*2^3 + 5*2^4 + 6*2^5 + 7*2^6 = 769 is prime. Other primes begin a(6) = 380713, a(12) = 22505929, a(26) = 2236055953, a(38) = 21562615273, a(44) = 51802781449, a(52) = 140712620569.
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FORMULA
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a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6.
O.g.f.: -12636/(-1+x)^4 -4/(-1+x) -21480/(-1+x)^5 -309/(-1+x)^2 -16920/(-1+x)^6 -3342/(-1+x)^3-5040/(-1+x)^7 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 26 2008
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CROSSREFS
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Cf. A000012, A005408, A056109, A056578, A056579.
Sequence in context: A012808 A097834 A063817 this_sequence A097311 A009972 A114037
Adjacent sequences: A113529 A113530 A113531 this_sequence A113533 A113534 A113535
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 12 2006
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