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%I #15 Mar 31 2024 08:45:34
%S 1,2,4,12,84,588,18228,565068,119229348,25157392428,5308209802308,
%T 1120032268286988,2588394572011229268,5981779855917950838348,
%U 179638830853071981626428788,5394733729348604680223282932428,162009248626067947151785409743745268
%N Sum of the absolute values in row n of A118686.
%H G. C. Greubel, <a href="/A119489/b119489.txt">Table of n, a(n) for n = 0..75</a>
%F a(n) = Sum_{k=0..n} abs( A118686(n,k) ).
%t g[n_]:= If[PrimeQ[n], n, 1]; p[n_]:= p[n]= If[n==0,1,g[n]*p[n-1]];
%t A119489= Flatten[Join[{{1}}, Table[Apply[Plus, Abs[Reverse[ CoefficientList[Product[x-p[n], {n,0,m}], x]]]], {m,0,30}]]]
%o (Magma)
%o R<x>:=PowerSeriesRing(Rationals(), 50);
%o g:= func< n | IsPrime(n) select n else 1 >;
%o p:=[1] cat [n le 1 select 1 else g(n)*Self(n-1): n in [1..50]];
%o T:= func< n,k | k eq 0 select 1 else Coefficient(R!( (&*[x-p[j+1]: j in [0..n-1]]) ), n-k) >;
%o [(&+[Abs(T(n,k)): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Mar 31 2024
%o (SageMath)
%o def g(n): return n if is_prime(n) else 1
%o def p(n): return 1 if n==0 else g(n)*p(n-1)
%o def T(n,k): return 1 if k==0 else ( product(x-p(j) for j in range(n)) ).series(x, n+2).list()[n-k] # T = A118686
%o [sum(abs(T(n,k)) for k in range(n+1)) for n in range(31)] # _G. C. Greubel_, Mar 31 2024
%Y Cf. A118686.
%K nonn
%O 0,2
%A _Roger L. Bagula_, May 25 2006
%E Terms a(12) onward added by _G. C. Greubel_, Mar 31 2024
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