A033792 - OEIS

%I #22 Jun 23 2017 00:57:27

%S 1,1,0,2,1,0,2,0,0,2,2,1,2,1,2,3,0,2,2,2,2,4,0,1,4,0,2,0,2,2,4,2,2,4,

%T 2,3,6,3,0,8,1,2,6,4,3,7,4,4,8,0,4,7,4,2,8,2,5,9,2,4,1,4,4,8,6,4,12,2,

%U 3,12,4,1,10,5,4,10,4,6,12,6,4,11,0,2,15,6

%N Product t2(q^d); d | 33, where t2(q) = theta2(q)/(2*q^(1/4)).

%C The above function t2 simplifies to t2(z) = 1 + z^2 + z^6 + z^12 + ... = sum_{n>=0} z^(n(n+1)) = sum_{n>=0} z^A002378(n). But the sequence lists only the coefficients of even powers, i.e., with t2 replaced by t(z) = 1 + z + z^3 + z^6 + ..., cf. formula. - _M. F. Hasler_, Oct 17 2014

%H Seiichi Manyama, <a href="/A033792/b033792.txt">Table of n, a(n) for n = 0..10000</a>

%F Coefficients of product_{d|33} t(x^d), with t(z) = sum_{n>=0} z^(n(n+1)/2) = sum_{n>=0} z^A000217(n). - _M. F. Hasler_, Oct 17 2014

%o (PARI) my(x='x+O('x^99), t(z)=sum(i=0, 10, z^((i+1)*i/2))); Vec(prod(i=1,#d=divisors(33), t(x^d[i]))) \\ _M. F. Hasler_, Oct 17 2014

%K nonn

%O 0,4

%A _N. J. A. Sloane_

%E More terms from _Seiichi Manyama_, May 24 2017