A011195 a(n) = n*(n+1)*(2*n+1)*(3*n+1)/6.

0, 4, 35, 140, 390, 880, 1729, 3080, 5100, 7980, 11935, 17204, 24050, 32760, 43645, 57040, 73304, 92820, 115995, 143260, 175070, 211904, 254265, 302680, 357700, 419900, 489879, 568260, 655690, 752840, 860405, 979104, 1109680, 1252900, 1409555, 1580460, 1766454

Offset

0,2

Links

Ivan Panchenko, 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.: x*(4 +15*x +5*x^2)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

E.g.f.: x*(24 + 81*x + 47*x^2 + 6*x^3)*exp(x)/6. - G. C. Greubel, Mar 03 2020

From Amiram Eldar, Mar 10 2022: (Start)

Sum_{n>=1} 1/a(n) = 36 - 9*sqrt(3)*Pi/2 + 48*log(2) - 81*log(3)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (9*sqrt(3)-12)*Pi - 36*(1-log(2)). (End)

Maple

seq( n*mul(j*n+1, j=1..3)/6, n=0..40); # G. C. Greubel, Mar 03 2020

Mathematica

Table[n(n+1)(2n+1)(3n+1)/6, {n, 0, 40}]  (* Harvey P. Dale, Feb 24 2011 *)

Prog

(PARI) vector(41, n, my(m=n-1); m*prod(j=1, 3, j*m+1)/6) \\ G. C. Greubel, Mar 03 2020
(Magma) [n*(&*[j*n+1:j in [1..3]])/6: n in [0..40]]; // G. C. Greubel, Mar 03 2020
(Sage) [n*product(j*n+1 for j in (1..3))/6 for n in (0..40)] # G. C. Greubel, Mar 03 2020
(GAP) List([0..40], n-> n*(n+1)*(2*n+1)*(3*n+1)/6 ); # G. C. Greubel, Mar 03 2020

Crossrefs

Cf. A094323.

Sequence in context: A228887 A185592 A296280 * A025195 A350407 A362346

Adjacent sequences: A011192 A011193 A011194 * A011196 A011197 A011198

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved