A341241 - OEIS

%I #8 Feb 20 2021 06:29:23

%S 1,0,3,3,6,9,13,21,27,40,54,75,97,129,171,220,282,360,460,576,720,896,

%T 1116,1374,1682,2061,2517,3050,3684,4449,5354,6414,7656,9135,10875,

%U 12891,15243,18015,21243,24966,29286,34326,40156,46851,54573,63509,73794,85551,99035,114555

%N Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^3.

%F G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^3.

%F a(n) ~ A107635(n). - _Vaclav Kotesovec_, Feb 20 2021

%p g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]

%p       [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)

%p     end:

%p b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),

%p       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))

%p     end:

%p a:= n-> b(n, 3):

%p seq(a(n), n=3..52);  # _Alois P. Heinz_, Feb 07 2021

%t nmax = 52; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &

%Y Cf. A000700, A022598, A047655, A107635, A327381, A338463, A341221, A341243, A341244, A341245, A341246, A341247, A341251.

%K nonn

%O 3,3

%A _Ilya Gutkovskiy_, Feb 07 2021