[go: up one dir, main page]

login
A350249
a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^2) + 1 + 1/x^(k^2)).
9
1, 1, 1, 1, 1, 3, 7, 19, 43, 95, 189, 429, 1003, 2457, 6319, 16165, 41601, 107969, 280253, 737065, 1950865, 5201941, 13954313, 37593679, 101695957, 276296549, 753191093, 2061201397, 5658850121, 15583938539, 43040609115, 119182143639, 330841253283, 920550527585
OFFSET
0,6
LINKS
FORMULA
Conjecture: a(n) ~ sqrt(5) * 3^(n + 1/2) / (2*sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, Feb 04 2022
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
expand((x^(n^2)+1+1/x^(n^2))*b(n-1)))
end:
a:= n-> coeff(b(n), x, 0):
seq(a(n), n=0..33); # Alois P. Heinz, Jan 28 2022
MATHEMATICA
Table[Coefficient[Product[x^(k^2) + 1 + 1/x^(k^2), {k, 1, n}], x, 0], {n, 0, 30}] (* Vaclav Kotesovec, Feb 05 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 28 2022
STATUS
approved