A350495 a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^2) + 1/x^(k^2))^2.

1, 2, 4, 8, 16, 40, 88, 222, 570, 1564, 4516, 13874, 41866, 137432, 442964, 1492610, 4998674, 17204844, 59175316, 207299554, 727137516, 2582078416, 9179001124, 32943918428, 118453240846, 428937325964, 1556421977612, 5676923326262, 20754245720206

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

Conjecture: a(n) ~ sqrt(5) * 4^n / (sqrt(Pi) * n^(5/2)). - Vaclav Kotesovec, Feb 05 2022

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      expand((x^(n^2)+1/x^(n^2))^2*b(n-1)))
    end:
a:= n-> coeff(b(n), x, 0):
seq(a(n), n=0..28);  # Alois P. Heinz, Jan 28 2022

Mathematica

Table[Coefficient[Product[(x^(k^2) + 1/x^(k^2))^2, {k, 1, n}], x, 0], {n, 0, 30}] (* Vaclav Kotesovec, Feb 05 2022 *)

Crossrefs

Cf. A000980, A047653, A158092, A350249, A350881.

Sequence in context: A344491 A028497 A197244 * A337581 A259377 A275071

Adjacent sequences: A350492 A350493 A350494 * A350496 A350497 A350498

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 28 2022

Status

approved