A094323 a(n) = n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/30.

0, 4, 63, 364, 1326, 3696, 8645, 17864, 33660, 59052, 97867, 154836, 235690, 347256, 497553, 695888, 952952, 1280916, 1693527, 2206204, 2836134, 3602368, 4525917, 5629848, 6939380, 8481980, 10287459, 12388068, 14818594, 17616456, 20821801, 24477600, 28629744

Offset

0,2

Links

Table of n, a(n) for n=0..32.

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

Formula

From Amiram Eldar, Mar 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 300 + (135*sqrt(3)/2 - 160)*Pi - 1200*log(2) + 1215*log(3)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (60 + 160*sqrt(2) - 135*sqrt(3))*Pi + (160*sqrt(2) - 380)*log(2) - 320*sqrt(2)*log(2-sqrt(2)) - 300. (End)

From Elmo R. Oliveira, May 25 2026: (Start)

G.f.: x*(4 + 39*x + 46*x^2 + 7*x^3)/(1 - x)^6.

E.g.f.: x*(120 + 825*x + 935*x^2 + 290*x^3 + 24*x^4)*exp(x)/30.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

a(n) = A011197(n)/5. (End)

Example

a(4) = 4*5*9*13*17/30 = 1326.

Mathematica

a[n_] := n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/30; Array[a, 30, 0] (* Amiram Eldar, Mar 08 2022 *)

Prog

(PARI) a(n) = n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/30; \\ Michel Marcus, Aug 15 2013

Crossrefs

Cf. A011195, A011197.

Sequence in context: A102196 A102192 A102197 * A286438 A224249 A361140

Adjacent sequences: A094320 A094321 A094322 * A094324 A094325 A094326

Keyword

easy,nonn

Author

Miklos Kristof, Jun 03 2004

Extensions

More terms from Michel Marcus, Aug 15 2013

Status

approved