A341225 - OEIS

A341225

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

%I #8 Feb 07 2021 11:49:48

%S 1,12,78,370,1437,4848,14719,41148,107610,266296,628941,1427118,

%T 3127369,6646440,13746081,27744926,54782271,106029918,201512970,

%U 376630680,693161334,1257641676,2251764699,3982196910,6961522279,12038699766,20607718317,34938910360

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

%H Alois P. Heinz, <a href="/A341225/b341225.txt">Table of n, a(n) for n = 6..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, 6):

%p seq(a(n), n=6..33); # _Alois P. Heinz_, Feb 07 2021

%t nmax = 33; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

%Y Column k=6 of A060642.

%Y Cf. A000041, A023005, A048574, A327384, A341221, A341222, A341223, A341226, A341227, A341228.

%K nonn

%O 6,2

%A _Ilya Gutkovskiy_, Feb 07 2021