OFFSET
0,3
LINKS
G. C. Greubel, Rows n = 0..30 of the triangle, flattened
FORMULA
T(n, k) = [x^k]( Product_{j=1..n} (1 - p(j)*x) ), where p(n) = Prime(n)*p(n-1) and p(1) = 2.
T(n, n) = A006939(n).
EXAMPLE
Triangle begins as:
1;
1, -2;
1, -8, 12;
1, -38, 252, -360;
1, -248, 8232, -53280, 75600;
1, -2558, 581112, -19069200, 123152400, -174636000;
MATHEMATICA
p[n_]:= p[n]= If[n==1, 2, Prime[n]*p[n-1]]; (* p = A002110 *)
Table[CoefficientList[Product[1 - p[j]*x, {j, n}], x], {n, 0, 12}]
PROG
(Magma)
m:=15;
function A002110(n)
if n eq 1 then return 2;
else return NthPrime(n)*A002110(n-1);
end if; return A002110;
end function;
f:= func< n, x | n eq 0 select 1 else (&*[(1 - A002110(j)*x): j in [1..n]]) >;
R<x>:=PowerSeriesRing(Integers(), m+2);
T:= func< n | Coefficients(R!( f(n, x) )) >;
[T(n): n in [0..m]]; // G. C. Greubel, Dec 09 2022
(SageMath)
def p(n): return 2 if (n==1) else nth_prime(n)*p(n-1) # p = A002110
def f(n, x): return product((1 - p(j)*x) for j in range(1, n+1))
def A118708(n, k): return 1 if (n==0) else ( f(n, x) ).series(x, n+1).list()[k]
flatten([[A118708(n, k) for k in range(n+1)] for n in range(16)]) # G. C. Greubel, Dec 09 2022
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, May 20 2006
EXTENSIONS
Edited by G. C. Greubel, Dec 09 2022
STATUS
approved