A341386 - OEIS

%I #9 Feb 10 2021 18:14:38

%S 1,8,44,184,662,2120,6256,17276,45277,113568,274592,643220,1465838,

%T 3260428,7097338,15153288,31791822,65645360,133584864,268213400,

%U 531879490,1042657088,2022113788,3882468712,7384455791,13921287616,26026092198,48273051172,88868177735

%N Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^4.

%H Alois P. Heinz, <a href="/A341386/b341386.txt">Table of n, a(n) for n = 4..10000</a>

%p g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/

%p      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)

%p     end:

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

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

%p     end:

%p a:= n-> b(n, 4):

%p seq(a(n), n=4..32);  # _Alois P. Heinz_, Feb 10 2021

%t nmax = 32; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^4, {x, 0, nmax}], x] // Drop[#, 4] &

%Y Cf. A026007, A027906, A321949, A327382, A341384, A341385, A341387, A341388, A341390, A341391.

%K nonn

%O 4,2

%A _Ilya Gutkovskiy_, Feb 10 2021