cp's OEIS Frontend

A161807 A trisection of A161804: a(n) = A161804(3n+2) for n>=0.

%I A161807 #2 Mar 30 2012 18:37:17
%S A161807 3,27,111,378,1356,4131,10881,29106,73500,167643,382053,849339,
%T A161807 1754061,3605094,7330311,14094945,26980563,51481332,93965784,
%U A161807 170910270,311155296,545970024,955201653,1676274750,2849709768,4831999623
%N A161807 A trisection of A161804: a(n) = A161804(3n+2) for n>=0.
%C A161807 G.f. of A161804 is exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ),
%C A161807 where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and
%C A161807 A038500(n) is the highest power of 3 dividing n.
%e A161807 G.f.: T_2(q) = 3 + 27*q + 111*q^2 + 378*q^3 + 1356*q^4 + 4131*q^5 +...
%e A161807 Terms are divisible by 3:
%e A161807 A/3=[1,9,37,126,452,1377,3627,9702,24500,55881,127351,283113,...].
%o A161807 (PARI) {a(n)=local(L=sum(m=1, 3*n+2,3*3^valuation(m,3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n+2))); polcoeff(exp(L), 3*n+2)}
%Y A161807 Cf. A161804, other trisections: A161805 (T_0), A161806 (T_1).
%K A161807 nonn
%O A161807 0,1
%A A161807 _Paul D. Hanna_, Jul 20 2009