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A triangular array made from polynomial coefficients of A049614.
2

%I #17 Feb 07 2021 21:07:34

%S 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 129,-72,16,1,-36,342,-1412,2913,-3168,1744,-384,1,-60,1206,-9620,

%U 36801,-73080,77776,-42240,9216,1,-252,12726,-241172,1883841,-7138872,14109136,-14975232,8119296,-1769472

%N A triangular array made from polynomial coefficients of A049614.

%C Same as an alternating sign Pascal's triangle up to row n=4.

%H G. C. Greubel, <a href="/A118687/b118687.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = coefficients of Product_{k=0..n} (1 - A049614(k)*x), with T(0, 0) = 1.

%e Triangle begins as:

%e 1;

%e 1, -1;

%e 1, -2, 1;

%e 1, -3, 3, -1;

%e 1, -4, 6, -4, 1;

%e 1, -8, 22,-28, 17, -4;

%t A049614[n_]:= n!/Product[Prime[i], {i, 1, PrimePi[n]}];

%t Join[{{1}}, Table[CoefficientList[Product[1 - A049614[k]*x, {k, 0, n}], x], {n, 0, 12}]]//Flatten

%o (Sage)

%o def A049614(n): return factorial(n)/product( nth_prime(j) for j in (1..prime_pi(n)) )

%o [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 Cf. A008275, A034386, A049614, A119490.

%K sign,tabl,less

%O 0,5

%A _Roger L. Bagula_, May 20 2006

%E Edited by _G. C. Greubel_, Feb 05 2021