A341245 - OEIS

%I #6 Feb 07 2021 13:57:58

%S 1,0,6,6,21,36,71,132,222,392,633,1038,1629,2544,3885,5842,8691,12738,

%T 18494,26520,37722,53132,74235,102882,141579,193506,262713,354552,

%U 475749,634932,842922,1113630,1464450,1917254,2499330,3244998,4196966,5408004,6943632,8884996

%N Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^6.

%F G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^6.

%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, 6):

%p seq(a(n), n=6..45);  # _Alois P. Heinz_, Feb 07 2021

%t nmax = 45; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

%Y Cf. A000700, A001484, A022601, A112150, A327384, A338463, A341225, A341241, A341243, A341244, A341246, A341247, A341251.

%K nonn

%O 6,3

%A _Ilya Gutkovskiy_, Feb 07 2021