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URL: https://oeis.org/A249076

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