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A161715
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(50*n^7 - 1197*n^6 + 11333*n^5 - 53655*n^4 + 132125*n^3 - 156828*n^2 + 73212*n + 5040)/5040
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21
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1, 2, 3, 5, 6, 10, 15, 30, 171, 886, 3359, 10143, 26072, 59502, 123931, 240048, 438261, 761754, 1270123, 2043641, 3188202, 4840994, 7176951, 10416034, 14831391, 20758446, 28604967, 38862163, 52116860, 69064806, 90525155, 117456180
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| {a(k): 0 <= k < 8} = divisors of 30:
a(n) = A027750(A006218(29) + k + 1), 0 <= k < A000005(30).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
R. Zumkeller, Enumerations of Divisors
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FORMULA
| a(n) = C(n,0) + C(n,1) + C(n,3) - 3*C(n,4) + 9*C(n,5) - 21*C(n,6) + 50*C(n,7).
G.f.: (1-6*x+15*x^2-19*x^3+8*x^4+18*x^5-51*x^6+84*x^7)/(-1+x)^8. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2009]
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EXAMPLE
| Differences of divisors of 30 to compute the coefficients of their interpolating polynomial, see formula:
.1 ... 2 ... 3 ... 5 ... 6 .. 10 .. 15 .. 30
... 1 ... 1 ... 2 ... 1 ... 4 ... 5 .. 15
...... 0 ... 1 .. -1 ... 3 ... 1 .. 10
......... 1 .. -2 ... 4 .. -2 ... 9
........... -3 ... 6 .. -6 .. 11
............... 9 . -12 .. 17
................ -21 .. 29
.................... 50.
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PROG
| (MAGMA) [(50*n^7 - 1197*n^6 + 11333*n^5 - 53655*n^4 + 132125*n^3 - 156828*n^2 + 73212*n + 5040)/5040: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011
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CROSSREFS
| A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A080856, A161711, A161712, A161713, A006261.
A018255, A161700, A161856. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 21 2009]
Sequence in context: A018255 A194358 A018727 * A164523 A033159 A199366
Adjacent sequences: A161712 A161713 A161714 * A161716 A161717 A161718
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009
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