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 A118708 Triangle, T(n, k) is the coefficient of x^k in ( Product_{j=1..n} (1 - A002110(j)*x) ), read by rows. 1
 1, 1, -2, 1, -8, 12, 1, -38, 252, -360, 1, -248, 8232, -53280, 75600, 1, -2558, 581112, -19069200, 123152400, -174636000, 1, -32588, 77397852, -17469862560, 572771228400, -3698441208000, 5244319080000, 1, -543098, 16713897732, -39529847287080, 8919112306734000, -292409138251692000, 1888096465415160000, -2677277333530800000 (list; table; graph; refs; listen; history; text; internal format)
 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:=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 Cf. A002110, A006939, A034386. Sequence in context: A007026 A160485 A328821 * A055134 A137370 A214272 Adjacent sequences: A118705 A118706 A118707 * A118709 A118710 A118711 KEYWORD sign,tabl AUTHOR Roger L. Bagula, May 20 2006 EXTENSIONS Edited by G. C. Greubel, Dec 09 2022 STATUS approved

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Last modified April 2 00:42 EDT 2023. Contains 361723 sequences. (Running on oeis4.)