A369494 a(n) = [x^(n*(n+1)/2)] Product_{k=1..n} (x^(k*(k+1)/2) + 1/x^(k*(k+1)/2)).

1, 1, 0, 0, 0, 2, 0, 3, 3, 5, 0, 14, 23, 39, 0, 101, 161, 315, 0, 971, 1595, 2872, 0, 9697, 17431, 31736, 0, 103608, 190242, 356883, 0, 1218049, 2235343, 4165201, 0, 14602056, 27304610, 51182196, 0, 179995388, 339041695, 640927871, 0, 2288387318, 4326722468, 8201714149

Offset

0,6

Links

Table of n, a(n) for n=0..45.

Maple

b:= proc(n, i) option remember; (m-> `if`(n>m, 0,
     `if`(n=m, 1, b(abs(n-i*(i+1)/2), i-1)+
        b(n+i*(i+1)/2, i-1))))((2+(3+i)*i)*i/6)
    end:
a:= n-> `if`(irem(n, 4)=2, 0, b(n*(n+1)/2, n)):
seq(a(n), n=0..45);  # Alois P. Heinz, Jan 24 2024

Mathematica

Table[Coefficient[Product[x^(k (k + 1)/2) + 1/x^(k (k + 1)/2), {k, 1, n}], x, n (n + 1)/2], {n, 0, 45}]

Crossrefs

Cf. A000217, A063890, A158380, A351002, A368243.

Sequence in context: A291304 A245332 A202035 * A343762 A247508 A112239

Adjacent sequences: A369491 A369492 A369493 * A369495 A369496 A369497

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2024

Status

approved