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A321948 Column k=3 of triangle A257673.

%I A321948 #10 Jan 30 2021 22:50:10
%S A321948 1,9,45,174,576,1719,4761,12441,31050,74593,173547,392787,867876,
%T A321948 1877322,3984636,8314434,17082510,34604523,69194309,136709688,
%U A321948 267111510,516515227,989147760,1877103486,3531796959,6591644601,12208734552,22449066710,40995144288
%N A321948 Column k=3 of triangle A257673.
%H A321948 Alois P. Heinz, <a href="/A321948/b321948.txt">Table of n, a(n) for n = 3..5000</a>
%F A321948 G.f.: (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^3. - _Ilya Gutkovskiy_, Jan 30 2021
%p A321948 b:= proc(n, k) option remember; `if`(n=0, 1, k*add(
%p A321948       b(n-j, k)*numtheory[sigma][2](j), j=1..n)/n)
%p A321948     end:
%p A321948 a:= n-> (k-> add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(3):
%p A321948 seq(a(n), n=3..35);
%Y A321948 Column k=3 of A257673.
%K A321948 nonn
%O A321948 3,2
%A A321948 _Alois P. Heinz_, Nov 22 2018