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A161715 a(n) = (50*n^7 - 1197*n^6 + 11333*n^5 - 53655*n^4 + 132125*n^3 - 156828*n^2 + 73212*n + 5040)/5040.

%I A161715 #40 Nov 19 2022 10:02:12
%S A161715 1,2,3,5,6,10,15,30,171,886,3359,10143,26072,59502,123931,240048,
%T A161715 438261,761754,1270123,2043641,3188202,4840994,7176951,10416034,
%U A161715 14831391,20758446,28604967,38862163,52116860,69064806,90525155,117456180
%N A161715 a(n) = (50*n^7 - 1197*n^6 + 11333*n^5 - 53655*n^4 + 132125*n^3 - 156828*n^2 + 73212*n + 5040)/5040.
%C A161715 {a(k): 0 <= k < 8} = divisors of 30:
%C A161715 a(n) = A027750(A006218(29) + k + 1), 0 <= k < A000005(30).
%H A161715 Vincenzo Librandi, <a href="/A161715/b161715.txt">Table of n, a(n) for n = 0..10000</a>
%H A161715 Reinhard Zumkeller, <a href="/A161700/a161700.txt">Enumerations of Divisors</a>
%H A161715 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A161715 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).
%F A161715 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
%F A161715 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
%e A161715 Differences of divisors of 30 to compute the coefficients of their interpolating polynomial, see formula:
%e A161715   1     2     3     5     6    10    15    30
%e A161715      1     1     2     1     4     5    15
%e A161715         0     1    -1     3     1    10
%e A161715            1    -2     4    -2     9
%e A161715              -3     6    -6    11
%e A161715                  9   -12    17
%e A161715                   -21    29
%e A161715                       50
%t A161715 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 *)
%o A161715 (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
%o A161715 (Python)
%o A161715 A161710_list, m = [1], [50, -321, 864, -1249, 1024, -452, 85, 1]
%o A161715 for _ in range(1,10**2):
%o A161715     for i in range(7):
%o A161715         m[i+1]+= m[i]
%o A161715     A161710_list.append(m[-1]) # _Chai Wah Wu_, Nov 09 2014
%o A161715 (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
%Y A161715 Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161701, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713.
%Y A161715 Cf. A018255, A161700, A161856. - _Reinhard Zumkeller_, Jun 21 2009
%K A161715 nonn,easy
%O A161715 0,2
%A A161715 _Reinhard Zumkeller_, Jun 17 2009