LINKS
Alois P. Heinz, <a href="/A369496/b369496_1.txt">Table of n, a(n) for n = 0..200</a>
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Alois P. Heinz, <a href="/A369496/b369496_1.txt">Table of n, a(n) for n = 0..200</a>
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Alois P. Heinz, <a href="/A369496/b369496_1.txt">Table of n, a(n) for n = 0..200</a>
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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
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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
0,5
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}]
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Ilya Gutkovskiy, Jan 24 2024
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