A369437 a(n) = [x^n] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

1, 1, 0, 0, 0, 0, 0, 4, 6, 15, 24, 40, 69, 138, 396, 1028, 3062, 8269, 21680, 50955, 115457, 262239, 631393, 1666438, 4558051, 12913587, 35530351, 95825467, 246943968, 628040166, 1607703060, 4228528070, 11485131123, 31616483271, 88141192570, 243487667830

Offset

0,8

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..108

Maple

b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 23 2024

Mathematica

Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, n], {n, 0, 34}]

Crossrefs

Cf. A000578, A316706, A348892, A369345.

Sequence in context: A034765 A300276 A109731 * A027631 A128620 A358438

Adjacent sequences: A369434 A369435 A369436 * A369438 A369439 A369440

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 23 2024

Status

approved