A011199 a(n) = (n+1)*(2*n+1)*(3*n+1).

1, 24, 105, 280, 585, 1056, 1729, 2640, 3825, 5320, 7161, 9384, 12025, 15120, 18705, 22816, 27489, 32760, 38665, 45240, 52521, 60544, 69345, 78960, 89425, 100776, 113049, 126280, 140505, 155760, 172081, 189504, 208065, 227800, 248745, 270936, 294409, 319200

Offset

0,2

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: (1 + 20*x + 15*x^2)/(x-1)^4. - Alois P. Heinz, Sep 04 2014

a(n) = 6*n^3 + 11*n^2 + 6*n + 1. - Reinhard Zumkeller, Jun 08 2015

E.g.f.: (1 + 23*x + 29*x^2 + 6*x^3)*exp(x). - G. C. Greubel, Mar 03 2020

From Amiram Eldar, Jan 13 2021: (Start)

Sum_{n>=0} 1/a(n) = sqrt(3)*Pi/4 - 4*log(2) + 9*log(3)/4.

Sum_{n>=0} (-1)^n/a(n) = 2*log(2) - (1 - sqrt(3)/2)*Pi. (End)

Maple

seq(mul(j*n+1, j=1..3), n = 0..40); # G. C. Greubel, Mar 03 2020

Mathematica

Product[j*Range[0, 40] +1, {j, 3}] (* G. C. Greubel, Mar 03 2020 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 24, 105, 280}, 40] (* Harvey P. Dale, Apr 21 2020 *)

Prog

(Haskell)
a011199 n = product $ map ((+ 1) . (* n)) [1, 2, 3]
-- Reinhard Zumkeller, Jun 08 2015
(PARI) vector(41, n, my(m=n-1); prod(j=1, 3, j*m+1)) \\ G. C. Greubel, Mar 03 2020
(Magma) [&*[j*n+1:j in [1..3]]: n in [0..40]]; // G. C. Greubel, Mar 03 2020
(Sage) [product(j*n+1 for j in (1..3)) for n in (0..40)] # G. C. Greubel, Mar 03 2020
(GAP) List([0..40], n-> (n+1)*(2*n+1)*(3*n+1) ); # G. C. Greubel, Mar 03 2020

Crossrefs

Cf. A079588.

Sequence in context: A027265 A044275 A044656 * A213874 A100149 A013980

Adjacent sequences: A011196 A011197 A011198 * A011200 A011201 A011202

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved