OFFSET
0,2
COMMENTS
This is the sequence (2^5)*A059860(n)= (2*binomial(n+1,2))^5, n >= 0. - Wolfdieter Lang, Nov 03 2014
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
FORMULA
a(n) = A002378(n)^5.
a(n) = 32*A059860(n) for n>0.
G.f.: 32*x*(x^8 + 232*x^7 + 5158*x^6 + 27664*x^5 + 47290*x^4 + 27664*x^3 + 5158*x^2 + 232*x + 1) / (1 - x)^11 (from A059860).
Sum_{n>=1} 1/a(n) = 126 - 35*Pi^2/3 - Pi^4/9. - Vaclav Kotesovec, Sep 25 2019
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11). - Wesley Ivan Hurt, Jan 20 2024
MAPLE
[ seq(n^5*(n+1)^5, n = 0..100) ];
MATHEMATICA
Table[(n (n + 1))^5, {n, 0, 70}] (* or *) CoefficientList[Series[32 x (x^8 + 232 x^7 + 5158 x^6 + 27664 x^5 + 47290 x^4 + 27664 x^3 + 5158 x^2 + 232 x + 1)/(1 - x)^11, {x, 0, 30}], x]
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 32, 7776, 248832, 3200000, 24300000, 130691232, 550731776, 1934917632, 5904900000, 16105100000}, 20] (* Harvey P. Dale, Apr 23 2017 *)
PROG
(Magma) [(n*(n+1))^5: n in [0..30]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eugene Chong, Oct 16 2014
EXTENSIONS
Terms a(32) and beyond corrected by Andrew Howroyd, Feb 20 2018
STATUS
approved