A119489 Sum of the absolute values in row n of A118686.

1, 2, 4, 12, 84, 588, 18228, 565068, 119229348, 25157392428, 5308209802308, 1120032268286988, 2588394572011229268, 5981779855917950838348, 179638830853071981626428788, 5394733729348604680223282932428, 162009248626067947151785409743745268

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..75

Formula

a(n) = Sum_{k=0..n} abs( A118686(n,k) ).

Mathematica

g[n_]:= If[PrimeQ[n], n, 1]; p[n_]:= p[n]= If[n==0, 1, g[n]*p[n-1]];
A119489= Flatten[Join[{{1}}, Table[Apply[Plus, Abs[Reverse[ CoefficientList[Product[x-p[n], {n, 0, m}], x]]]], {m, 0, 30}]]]

Prog

(Magma)
R<x>:=PowerSeriesRing(Rationals(), 50);
g:= func< n | IsPrime(n) select n else 1 >;
p:=[1] cat [n le 1 select 1 else g(n)*Self(n-1): n in [1..50]];
T:= func< n, k | k eq 0 select 1 else Coefficient(R!( (&*[x-p[j+1]: j in [0..n-1]]) ), n-k) >;
[(&+[Abs(T(n, k)): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 31 2024
(SageMath)
def g(n): return n if is_prime(n) else 1
def p(n): return 1 if n==0 else g(n)*p(n-1)
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
[sum(abs(T(n, k)) for k in range(n+1)) for n in range(31)] # G. C. Greubel, Mar 31 2024

Crossrefs

Cf. A118686.

Sequence in context: A002080 A001206 A144295 * A353743 A217757 A053631

Adjacent sequences: A119486 A119487 A119488 * A119490 A119491 A119492

Keyword

nonn

Author

Roger L. Bagula, May 25 2006

Extensions

Terms a(12) onward added by G. C. Greubel, Mar 31 2024

Status

approved