A369495 a(n) = [x^n] Product_{k=1..n} (x^(k*(k+1)/2) + 1 + 1/x^(k*(k+1)/2)).

1, 1, 1, 2, 3, 5, 11, 25, 56, 129, 313, 748, 1831, 4584, 11581, 29555, 76398, 199191, 522746, 1382158, 3676072, 9828631, 26412174, 71310248, 193346941, 526302232, 1437895915, 3941671019, 10839118898, 29893768219, 82671240995, 229213877639, 637049969282

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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$2):
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, 0, 32}]

Crossrefs

Cf. A000217, A316706, A351002, A369344, A369433.

Sequence in context: A076051 A000628 A358554 * A273755 A258804 A006888

Adjacent sequences: A369492 A369493 A369494 * A369496 A369497 A369498

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2024

Status

approved