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Column k=9 of triangle A257673.
3

%I #10 Jan 31 2021 08:11:10

%S 1,27,378,3681,28134,180198,1007370,5051790,23173047,98644395,

%T 394006761,1489460724,5365964511,18526724685,61587671283,197885754837,

%U 616568620176,1868127089697,5517376711191,15917134652829,44935916034951,124340811582540,337706753653476

%N Column k=9 of triangle A257673.

%H Alois P. Heinz, <a href="/A321954/b321954.txt">Table of n, a(n) for n = 9..5000</a>

%F G.f.: (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^9. - _Ilya Gutkovskiy_, Jan 31 2021

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

%p b(n-j, k)*numtheory[sigma][2](j), j=1..n)/n)

%p end:

%p a:= n-> (k-> add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):

%p seq(a(n), n=9..35);

%Y Column k=9 of A257673.

%K nonn

%O 9,2

%A _Alois P. Heinz_, Nov 22 2018