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A118687 A triangular array made from polynomial coefficients of A049614.

%I A118687 #17 Feb 07 2021 21:07:34
%S A118687 1,1,-1,1,-2,1,1,-3,3,-1,1,-4,6,-4,1,1,-8,22,-28,17,-4,1,-12,54,-116,
%T A118687 129,-72,16,1,-36,342,-1412,2913,-3168,1744,-384,1,-60,1206,-9620,
%U A118687 36801,-73080,77776,-42240,9216,1,-252,12726,-241172,1883841,-7138872,14109136,-14975232,8119296,-1769472
%N A118687 A triangular array made from polynomial coefficients of A049614.
%C A118687 Same as an alternating sign Pascal's triangle up to row n=4.
%H A118687 G. C. Greubel, <a href="/A118687/b118687.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A118687 T(n, k) = coefficients of Product_{k=0..n} (1 - A049614(k)*x), with T(0, 0) = 1.
%e A118687 Triangle begins as:
%e A118687   1;
%e A118687   1, -1;
%e A118687   1, -2,  1;
%e A118687   1, -3,  3, -1;
%e A118687   1, -4,  6, -4,  1;
%e A118687   1, -8, 22,-28, 17, -4;
%t A118687 A049614[n_]:= n!/Product[Prime[i], {i, 1, PrimePi[n]}];
%t A118687 Join[{{1}}, Table[CoefficientList[Product[1 - A049614[k]*x, {k, 0, n}], x], {n, 0, 12}]]//Flatten
%o A118687 (Sage)
%o A118687 def A049614(n): return factorial(n)/product( nth_prime(j) for j in (1..prime_pi(n)) )
%o A118687 [1]+flatten([[( product(1 - A049614(k)*x for k in (0..n)) ).series(x,n+2).list()[k] for k in (0..n+1)] for n in (0..12)]) # _G. C. Greubel_, Feb 05 2021
%Y A118687 Cf. A008275, A034386, A049614, A119490.
%K A118687 sign,tabl,less
%O A118687 0,5
%A A118687 _Roger L. Bagula_, May 20 2006
%E A118687 Edited by _G. C. Greubel_, Feb 05 2021