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Column k=6 of triangle A257673.
3

%I #10 Jan 30 2021 22:50:28

%S 1,18,171,1158,6309,29466,122580,465738,1644516,5464892,17253369,

%T 52128540,151592391,426265836,1163373243,3091338000,8018585046,

%U 20348618814,50615278427,123608650182,296794147017,701525018576,1634144413185,3755097200094,8519488746222

%N Column k=6 of triangle A257673.

%H Alois P. Heinz, <a href="/A321951/b321951.txt">Table of n, a(n) for n = 6..5000</a>

%F G.f.: (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^6. - _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))(6):

%p seq(a(n), n=6..35);

%Y Column k=6 of A257673.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Nov 22 2018