A011197 a(n) = n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/6.

0, 20, 315, 1820, 6630, 18480, 43225, 89320, 168300, 295260, 489335, 774180, 1178450, 1736280, 2487765, 3479440, 4764760, 6404580, 8467635, 11031020, 14180670, 18011840, 22629585, 28149240, 34696900, 42409900, 51437295, 61940340, 74092970, 88082280, 104109005

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: 5*x*(4 + 39*x + 46*x^2 + 7*x^3)/(1-x)^6. - Alois P. Heinz, Sep 04 2014

E.g.f.: x*(120 + 825*x + 935*x^2 + 290*x^3 + 24*x^4)*exp(x)/6. - G. C. Greubel, Mar 03 2020

From Amiram Eldar, Mar 10 2022: (Start)

a(n) = 5 * A094323(n).

Sum_{n>=1} 1/a(n) = 60 + (27*sqrt(3)/2 - 32)*Pi - 240*log(2) + 243*log(3)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (12 + 32*sqrt(2) - 27*sqrt(3))*Pi + (32*sqrt(2) - 76)*log(2) - 64*sqrt(2)*log(2-sqrt(2)) - 60. (End)

Maple

seq( n*mul(j*n+1, j=1..4)/6, n = 0..30); # G. C. Greubel, Mar 03 2020

Mathematica

Table[n*Product[j*n+1, {j, 4}]/6, {n, 0, 30}] (* G. C. Greubel, Mar 03 2020 *)

Prog

(PARI) lista(nn) = vector(nn, i, n = i--; n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/6); \\ Michel Marcus, Sep 04 2014
(Magma) [n*(&*[j*n+1:j in [1..4]])/6: n in [0..30]]; // G. C. Greubel, Mar 03 2020
(Sage) [n*product(j*n+1 for j in (1..4))/6 for n in (0..30)] # G. C. Greubel, Mar 03 2020
(GAP) List([0..40], n-> n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/6 ); # G. C. Greubel, Mar 03 2020

Crossrefs

Cf. A094323.

Sequence in context: A240799 A281931 A034094 * A054621 A111778 A024387

Adjacent sequences: A011194 A011195 A011196 * A011198 A011199 A011200

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved