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a(n) = (n^43 - n)/42.
3

%I #16 Sep 08 2022 08:45:19

%S 0,0,209430786243,7815642080822311372,1842172677508006361457030,

%T 27068294695622864223661876860,68747114771196346634599779308105,

%U 51995580380757061883555053636996008

%N a(n) = (n^43 - n)/42.

%C Also integer sequences for (n^2-n)/1 (A002378 offset), (n^3-n)/2 (A027480 offset), (n^7-n)/6 (A108495) and (n^1807-n)/1806.

%H Vincenzo Librandi, <a href="/A108496/b108496.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Zagier, <a href="http://www-groups.mcs.st-andrews.ac.uk/~john/Zagier/Problems.html">Problems posed at the St Andrews Colloquium, 1996</a>.

%F a(n) = (n-1)*A108048(n).

%e a(2) = (2^43 - 2)/42 = 8796093022206/42 = 209430786243.

%t Table[(n^43-n)/42,{n,0,10}] (* _Harvey P. Dale_, Jan 31 2022 *)

%o (Magma) [(n^43-n)/42: n in [0..20]]; // _Vincenzo Librandi_, May 02 2011

%Y Cf. A014117, A108497, A108499.

%K nonn

%O 0,3

%A _Henry Bottomley_, Jun 06 2005