A369343 a(n) is the constant term in expansion of Product_{k=1..n} (x^(2*k-1) + 1 + 1/x^(2*k-1)).

1, 1, 1, 1, 3, 9, 21, 49, 117, 295, 761, 1993, 5261, 14025, 37699, 102151, 278587, 764145, 2106433, 5832863, 16217191, 45255167, 126708863, 355848715, 1002145705, 2829479797, 8007670701, 22711890561, 64547494347, 183790615881, 524239904367, 1497786769295

Offset

0,5

Comments

All terms are odd.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..630

Formula

a(n) ~ 3^(n+1) / (4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jan 21 2024

Maple

b:= proc(n, i) option remember; `if`(n>i^2, 0, `if`(i=0, 1,
      b(n, i-1)+b(n+2*i-1, i-1)+b(abs(n-2*i+1), i-1)))
    end:
a:= n-> b(0, n):
seq(a(n), n=0..33);  # Alois P. Heinz, Jan 21 2024

Mathematica

Table[Coefficient[Product[x^(2 k - 1) + 1 + 1/x^(2 k - 1), {k, 1, n}], x, 0], {n, 0, 30}]

Crossrefs

Cf. A005408, A007576, A156700, A292476.

Sequence in context: A006813 A274230 A056823 * A105544 A119917 A111209

Adjacent sequences: A369340 A369341 A369342 * A369344 A369345 A369346

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 20 2024

Status

approved