A119489 - OEIS

%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