%I #32 Dec 21 2023 11:32:01
%S 0,6,120,504,1320,2730,4896,7980,12144,17550,24360,32736,42840,54834,
%T 68880,85140,103776,124950,148824,175560,205320,238266,274560,314364,
%U 357840,405150,456456,511920,571704,635970,704880,778596,857280,941094
%N a(n) = 3*n*(3*n-1)*(3*n-2).
%D L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 46.
%D Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 268.
%H Konrad Knopp, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=b88432273f115fb346725f1a42422e19;c=umhistmath;idno=ACM1954.0001.001">Theorie und Anwendung der unendlichen Reihen</a>, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F a(n) = A007531(3n-2) = 6*A006566(n).
%F Sum_{n>=1} 1/a(n) = Pi*sqrt(3)/12 - log(3)/4 = 0.178796768891527... [Jolley eq. 250]. - _Benoit Cloitre_, Apr 05 2002
%F G.f.: 6*x*(1+16*x+10*x^2)/(1-x)^4.
%F E.g.f.: 3*exp(x)*x*(2 + 18x + 9x^2). - _Indranil Ghosh_, Apr 15 2017
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/3 - Pi/(6*sqrt(3)). - _Amiram Eldar_, Mar 08 2022
%p A054776:=n->3*n*(3*n-1)*(3*n-2): seq(A054776(n), n=0..50); # _Wesley Ivan Hurt_, Apr 14 2017
%o (PARI) a(n)=3*n*(3*n-1)*(3*n-2)
%Y Cf. A006566, A007531, A097321.
%K easy,nonn
%O 0,2
%A _Henry Bottomley_, May 19 2000