%I #9 Feb 05 2024 19:50:43

%S 1,1,1,1,2,4,8,20,47,104,246,607,1496,3751,9579,24720,64327,168932,

%T 446830,1188030,3177198,8541152,23063100,62550085,170337684,465564180,

%U 1276779917,3512617527,9692054125,26815357935,74381739478,206820705565,576371104028

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

%H Alois P. Heinz, <a href="/A369496/b369496.txt">Table of n, a(n) for n = 0..200</a>

%p b:= proc(n, i) option remember; (m-> `if`(n>m, 0,

%p `if`(n=m, 1, b(abs(n-i*(i+1)/2), i-1)+b(n, i-1)+

%p b(n+i*(i+1)/2, i-1))))((2+(3+i)*i)*i/6)

%p end:

%p a:= n-> b(n*(n+1)/2, n):

%p seq(a(n), n=0..32); # _Alois P. Heinz_, Jan 24 2024

%t 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}]

%Y Cf. A000217, A316706, A369344, A369434.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Jan 24 2024