login
Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^10.
3

%I #8 Feb 10 2021 19:05:32

%S 1,20,230,1940,13285,77944,405250,1910330,8300380,33655860,128574734,

%T 466317760,1615509765,5373215450,17230062315,53457917856,160963157005,

%U 471587847690,1347417640405,3761860656610,10280578499844,27543107112940,72440412567485

%N Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^10.

%H Alois P. Heinz, <a href="/A341394/b341394.txt">Table of n, a(n) for n = 10..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, 10):

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

%t nmax = 32; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &

%Y Cf. A026007, A321955, A327388, A341384, A341385, A341386, A341387, A341388, A341390, A341391, A341393.

%K nonn

%O 10,2

%A _Ilya Gutkovskiy_, Feb 10 2021