A249076 a(n) = (n*(n+1))^6.

0, 64, 46656, 2985984, 64000000, 729000000, 5489031744, 30840979456, 139314069504, 531441000000, 1771561000000, 5289852801024, 14412774445056, 36343632130624, 85766121000000, 191102976000000, 404961208827904, 820972403643456, 1600135042849344, 3010936384000000, 5489031744000000

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

a(n) = A002378(n)^6.

a(n) = 64*A059978(n) for n>0.

G.f.: 64*x*(x^10 + 716*x^9 + 37257*x^8 + 450048*x^7 + 1822014*x^6 + 2864328*x^5 + 1822014*x^4 + 450048*x^3 + 37257*x^2 + 716*x + 1)/(1 - x)^13. [corrected by Georg Fischer, May 10 2019]

Sum_{n>=1} 1/a(n) = -462 + 42*Pi^2 + 7*Pi^4/15 + 2*Pi^6/945. - Vaclav Kotesovec, Sep 25 2019

Maple

[ seq(n^6*(n+1)^6, n = 0..100) ];

Mathematica

Table[(n (n + 1))^6, {n, 0, 70}] (* or *)
CoefficientList[Series[64*x*(x^10 + 716 x^9 + 37257 x^8 + 450048 x^7 + 1822014 x^6 + 2864328 x^5 + 1822014 x^4 + 450048 x^3 + 37257 x^2 + 716 x + 1)/(1 - x)^13, {x, 0, 30}], x]

Prog

(Magma) [(n*(n+1))^6: n in [0..30]];
(PARI) a(n)=(n*(n+1))^6 \\ Charles R Greathouse IV, Oct 21 2014

Crossrefs

Cf. A059978; A002378: n*(n+1); A035282: n^2 *(n+1)^2; A060459: n^3 *(n+1)^3; A248619: n^4 *(n+1)^4;

Sequence in context: A141092 A283924 A016830 * A334605 A103346 A123394

Adjacent sequences: A249073 A249074 A249075 * A249077 A249078 A249079

Keyword

nonn,easy

Author

Jiwoo Lee, Oct 20 2014

Extensions

Incorrect term corrected by Colin Barker, Oct 21 2014

Terms a(21) and beyond corrected by Andrew Howroyd, Feb 22 2018

Status

approved