A350310 - OEIS

%I #45 Jan 16 2022 11:09:35

%S 1,-1,-2,-2,-1,0,2,4,6,7,8,8,6,4,0,-6,-11,-18,-26,-32,-38,-44,-46,-46,

%T -44,-37,-26,-12,8,32,58,90,124,158,194,228,259,286,306,316,316,304,

%U 276,232,170,88,-12,-132,-272,-431,-606,-794,-994,-1200,-1408,-1614,-1808,-1984,-2138,-2258,-2336

%N Alternating row sums of A066448.

%H Seiichi Manyama, <a href="/A350310/b350310.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k=0..n} (-1)^k * A066448(n,k).

%F G.f.: Sum_{k>=0} (-1)^k * x^(k^2) * Product_{j=1..k} (1+x^j)/(1-x^j).

%o (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=0, sqrtint(N), (-1)^k*x^k^2*prod(j=1, k, (1+x^j)/(1-x^j))))

%Y Cf. A039924, A066447, A066448, A237979, A350737, A350738.

%K sign

%O 0,3

%A _Seiichi Manyama_, Jan 12 2022