A161805 A trisection of A161804: a(n) = A161804(3n) for n>=0.

1, 12, 66, 255, 903, 2970, 8571, 23001, 59763, 145164, 333693, 751059, 1623009, 3363576, 6872307, 13677228, 26351985, 50309910, 94392525, 172538934, 313558506, 563064207, 988996095, 1730456433, 3001805067, 5106353439

Offset: 0

Author

Paul D. Hanna, Jul 20 2009

Keywords

• nonn

Comments

G.f. of A161804 is exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ),

where A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], and

A038500(n) is the highest power of 3 dividing n.

Examples

			G.f.: T_0(q) = 1 + 12*q + 66*q^2 + 255*q^3 + 903*q^4 + 2970*q^5 +...
		

Crossrefs

Cf. A161804, other trisections: A161806 (T_1), A161807 (T_2).

Programs

PARI

{a(n)=local(L=sum(m=1, 3*n,3*3^valuation(m,3)*sumdiv(m, d, -(-1)^d*d)*x^m/m)+x*O(x^(3*n))); polcoeff(exp(L), 3*n)}