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A161715
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a(n) = (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
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OFFSET
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0,2
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COMMENTS
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{a(k): 0 <= k < 8} = divisors of 30:
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LINKS
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FORMULA
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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. - R. J. Mathar, Jun 18 2009
a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8). - Wesley Ivan Hurt, Apr 26 2021
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EXAMPLE
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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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MATHEMATICA
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CoefficientList[Series[(1-6*x+15*x^2-19*x^3+8*x^4+18*x^5-51*x^6+84*x^7)/(-1+x)^8, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)
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PROG
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(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
(Python)
A161710_list, m = [1], [50, -321, 864, -1249, 1024, -452, 85, 1]
for _ in range(1, 10**2):
for i in range(7):
m[i+1]+= m[i]
(PARI) x='x+O('x^50); Vec((1 -6*x +15*x^2 -19*x^3 +8*x^4 +18*x^5 -51*x^6 +84*x^7) /(-1+x)^8) \\ G. C. Greubel, Jul 16 2017
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CROSSREFS
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Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161701, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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