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Column k=7 of triangle A257673.
3

%I #10 Jan 30 2021 22:50:34

%S 1,21,231,1792,11067,58044,268940,1129999,4385136,15928948,54711958,

%T 179090772,562156203,1700628930,4978677738,14153099499,39180254316,

%U 105881154624,279906223856,725158329175,1844006226090,4608929551309,11336379967178,27469729015029

%N Column k=7 of triangle A257673.

%H Alois P. Heinz, <a href="/A321952/b321952.txt">Table of n, a(n) for n = 7..5000</a>

%F G.f.: (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^7. - _Ilya Gutkovskiy_, Jan 30 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))(7):

%p seq(a(n), n=7..35);

%Y Column k=7 of A257673.

%K nonn

%O 7,2

%A _Alois P. Heinz_, Nov 22 2018