A369495 - OEIS

%I #6 Jan 25 2024 08:03:43

%S 1,1,1,2,3,5,11,25,56,129,313,748,1831,4584,11581,29555,76398,199191,

%T 522746,1382158,3676072,9828631,26412174,71310248,193346941,526302232,

%U 1437895915,3941671019,10839118898,29893768219,82671240995,229213877639,637049969282

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

%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$2):

%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, 0, 32}]

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

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jan 24 2024