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A113531
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1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5.
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1
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1, 21, 321, 2005, 7737, 22461, 54121, 114381, 219345, 390277, 654321, 1045221, 1604041, 2379885, 3430617, 4823581, 6636321, 8957301, 11886625, 15536757, 20033241, 25515421, 32137161, 40067565, 49491697, 60611301, 73645521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 1 + 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 is the derivative of 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 = (n^7 - 1)/(n-1). a(6) = 1 + 2*6 + 3*6^2 + 4*6^3 + 5*6^4 + 6*6^5 = 54121 is prime, the smallest prime in the sequence. The next is a(a(1)) = a(21) = 1 + 2*21 + 3*21^2 + 4*21^3 + 5*21^4 + 6*21^5 = 25515421. Then a(24) = 49491697.
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FORMULA
| a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5.
O.g.f.: 2064/(-1+x)^4+3/(-1+x)+2040/(-1+x)^5+132/(-1+x)^2+720/(-1+x)^6+872/(-1+x)^3 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 26 2008
a(0)=1, a(1)=21, a(2)=321, a(3)=2005, a(4)=7737, a(5)=22461, a(n)= 6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) [From Harvey P. Dale, Nov 02 2011]
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MATHEMATICA
| With[{eq=Total[# n^(#-1)&/@Range[6]]}, Table[eq, {n, 0, 30}]] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 21, 321, 2005, 7737, 22461}, 30] (* From Harvey P. Dale, Nov 02 2011 *)
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CROSSREFS
| Cf. A000012, A005408, A056109, A056578, A056579.
Sequence in context: A055434 A016315 A127424 * A069572 A057138 A104759
Adjacent sequences: A113528 A113529 A113530 * A113532 A113533 A113534
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 12 2006
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EXTENSIONS
| Corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 26 2008
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