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A166870 a(n) = n*(n-1)*A056219(n+1).

%I A166870 #21 Feb 18 2024 03:07:21
%S A166870 4,24,60,120,270,546,840,1368,2250,3740,5544,7956,11102,16380,23520,
%T A166870 33184,44676,59850,79420,106260,141834,189244,245088,314400,401050,
%U A166870 511758,648648,824992,1044000,1315020,1635808,2023296,2494206,3077340
%N A166870 a(n) = n*(n-1)*A056219(n+1).
%H A166870 G. C. Greubel, <a href="/A166870/b166870.txt">Table of n, a(n) for n = 2..1000</a>
%p A166870 N:= 100; b:= seq(coeff(series(add(x^((1/2)*n*(n+1))*mul(x +1/(1-x^k), k=1..n), n = 1..floor((1/2)*sqrt(9+8*N))), x, N+2), x, j), j = 1..N+1); seq(n*(n-1)*b[n+1], n=2..N); # _G. C. Greubel_, Nov 29 2019
%t A166870 max:= 100; b:= CoefficientList[Series[Sum[x^(n*(n+1)/2)*Product[(x +1/(1-x^k)), {k, n}], {n, Floor[Sqrt[9 +8*(max+5)]/2]}], {x, 0, max+5}], x]; Table[n*b[[n + 2]], {n, 2, max}] (* _G. C. Greubel_, Nov 29 2019 *)
%o A166870 (Magma)
%o A166870 max:=50;
%o A166870 R<x>:=PowerSeriesRing(Integers(), max); b:= Coefficients(R!( (&+[x^Binomial(n+1,2)*(&*[x + 1/(1-x^j): j in [1..n]]): n in [1..Floor(Sqrt(9+8*max)/2)]]) ));
%o A166870 [(n-1)*(n-2)*b[n]: n in [3..max-1]]; // _G. C. Greubel_, Nov 29 2019
%o A166870 (Sage)
%o A166870 max=50;
%o A166870 def A056219_list(prec):
%o A166870     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166870     return P( sum(x^binomial(n+1,2)*product((x + 1/(1-x^j)) for j in (1..n)) for n in (1..floor(sqrt(9+8*max)/2))) ).list()
%o A166870 b=A056219_list(max);
%o A166870 [(n-1)*(n-2)*b[n] for n in (3..max)] # _G. C. Greubel_, Nov 29 2019
%Y A166870 Cf. A056219, A166869.
%K A166870 nonn,less
%O A166870 2,1
%A A166870 _Roger L. Bagula_, Oct 22 2009