login
Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^7.
11

%I #8 Feb 07 2021 11:47:02

%S 1,14,105,567,2478,9317,31269,95965,273896,735966,1879059,4591342,

%T 10797290,24549924,54171729,116368308,243991034,500446135,1006039762,

%U 1985480063,3852429483,7358212272,13850448185,25718189483,47150564517,85417834621,153015826880

%N Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^7.

%H Alois P. Heinz, <a href="/A341226/b341226.txt">Table of n, a(n) for n = 7..10000</a>

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

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

%p end:

%p a:= n-> b(n, 7):

%p seq(a(n), n=7..33); # _Alois P. Heinz_, Feb 07 2021

%t nmax = 33; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &

%Y Column k=7 of A060642.

%Y Cf. A000041, A023006, A048574, A327385, A341221, A341222, A341223, A341225, A341227, A341228.

%K nonn

%O 7,2

%A _Ilya Gutkovskiy_, Feb 07 2021