A369496 a(n) = [x^(n*(n+1)/2)] Product_{k=1..n} (x^(k*(k+1)/2) + 1 + 1/x^(k*(k+1)/2)).

1, 1, 1, 1, 2, 4, 8, 20, 47, 104, 246, 607, 1496, 3751, 9579, 24720, 64327, 168932, 446830, 1188030, 3177198, 8541152, 23063100, 62550085, 170337684, 465564180, 1276779917, 3512617527, 9692054125, 26815357935, 74381739478, 206820705565, 576371104028

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

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-1)+
        b(n+i*(i+1)/2, i-1))))((2+(3+i)*i)*i/6)
    end:
a:= n-> b(n*(n+1)/2, n):
seq(a(n), n=0..32);  # Alois P. Heinz, Jan 24 2024

Mathematica

Table[Coefficient[Product[x^(k (k + 1)/2) + 1 + 1/x^(k (k + 1)/2), {k, 1, n}], x, n (n + 1)/2], {n, 0, 32}]

Crossrefs

Cf. A000217, A316706, A369344, A369434.

Sequence in context: A288476 A338197 A056952 * A225585 A121703 A301467

Adjacent sequences: A369493 A369494 A369495 * A369497 A369498 A369499

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2024

Status

approved