A161704 a(n) = (3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30.

1, 2, 3, 6, 9, 18, 59, 190, 513, 1186, 2435, 4566, 7977, 13170, 20763, 31502, 46273, 66114, 92227, 125990, 168969, 222930, 289851, 371934, 471617, 591586, 734787, 904438, 1104041, 1337394, 1608603, 1922094, 2282625, 2695298, 3165571, 3699270

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• nonn
• easy

Comments

{a(k): 0 <= k < 6} = divisors of 18:

a(n) = A027750(A006218(17) + k + 1), 0 <= k < A000005(18).

Examples

			Differences of divisors of 18 to compute the coefficients of their interpolating polynomial, see formula:
  1     2     3     6     9    18
     1     1     3     3     9
        0     2     0     6
           2    -2     6
             -4     8
                12
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• R. Zumkeller, Enumerations of Divisors
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A018251, A058331, A080856, A086514, A161701, A161702, A161703, A161706, A161707, A161708, A161710, A161711, A161712, A161713, A161715, A161856.

Programs

Magma

[(3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Maple

A161704:=n->(3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30: seq(A161704(n), n=0..50); # Wesley Ivan Hurt, Jul 16 2017

Mathematica

CoefficientList[Series[(1 - 4*x + 6*x^2 - 2*x^3 - 7*x^4 + 18*x^5)/(x - 1)^6, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)

PARI

a(n)=n*(3*n^4-35*n^3+145*n^2-235*n+152)/30+1

Formula

a(n) = C(n,0) + C(n,1) + 2*C(n,3) - 4*C(n,4) + 12*C(n,5).

G.f.: ( 1-4*x+6*x^2-2*x^3-7*x^4+18*x^5 ) / (x-1)^6. - R. J. Mathar, Jul 12 2016