A033592 a(n) = (2*n+1)*(3*n+1)*(4*n+1)*(5*n+1).

1, 360, 3465, 14560, 41769, 96096, 191425, 344520, 575025, 905464, 1361241, 1970640, 2764825, 3777840, 5046609, 6610936, 8513505, 10799880, 13518505, 16720704, 20460681, 24795520, 29785185, 35492520, 41983249, 49325976, 57592185, 66856240, 77195385

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (1 +355*x +1675*x^2 +825*x^3 +24*x^4)/(1-x)^5. - Colin Barker, Sep 04 2012

a(0)=1, a(1)=360, a(2)=3465, a(3)=14560, a(4)=41769, a(n) = 5*a(n-1)- 10*a(n-2) + 10*a(n-3) -5*a(n-4) +a(n-5). - Harvey P. Dale, Nov 28 2013

From G. C. Greubel, Mar 05 2020: (Start)

a(n) = n^4 * Pochhammer(2 + 1/n, 4).

E.g.f.: (1 + 359*x + 1373*x^2 + 874*x^3 + 120*x^4)*exp(x). (End)

Maple

1, seq( n^4*pochhammer(2+1/n, 4), n=1..30); # G. C. Greubel, Mar 05 2020

Mathematica

CoefficientList[Series[(1 + 355 x + 1675 x^2 + 825 x^3 + 24 x^4)/(1 - x)^5, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 20 2013 *)
Table[Times@@(n*Range[2, 5]+1), {n, 0, 30}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 360, 3465, 14560, 41769}, 30] (* Harvey P. Dale, Nov 28 2013 *)

Prog

(Magma) [(2*n+1)*(3*n+1)*(4*n+1)*(5*n+1): n in [0..30]]; // Vincenzo Librandi, Oct 20 2013
(PARI) vector(31, n, my(m=n-1); prod(j=2, 5, j*m+1)) \\ G. C. Greubel, Mar 05 2020
(Sage) [product(j*n+1 for j in (2..5)) for n in (0..30)] # G. C. Greubel, Mar 05 2020
(GAP) List([0..30], n-> Product([2..5], j-> j*n+1) ); # G. C. Greubel, Mar 05 2020

Crossrefs

Sequence in context: A234555 A234550 A024185 * A305626 A056322 A056313

Adjacent sequences: A033589 A033590 A033591 * A033593 A033594 A033595

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved