%I #11 May 15 2013 08:39:32
%S 1,1,-1,1,-2,1,1,-3,3,-1,1,-4,6,-4,1,1,-5,10,-10,5,-1,1,-10,35,-60,55,
%T -26,5,1,-15,85,-235,355,-301,135,-25,1,-20,160,-660,1530,-2076,1640,
%U -700,125,1,-25,260,-1460,4830,-9726,12020,-8900,3625,-625,1,-30,385,-2760,12130,-33876,60650,-69000,48125,-18750
%N Generalized Pascal's triangle made using Mod[(Prime[n] - 1)/2, 4] == 2 primorial-like Stirling polynomials.
%C Apparently the sequence is based on the list of primes p=5, 13, 29, 37, 53, 61,... for which (p-1)/2 == 2 (mod 4), derived from A005097. The coefficients of the polynomial of degree n are listed in row n, where the polynomial is a product of the form prod_i (1-p_i*x), and p_i is the largest prime of that modular subset which is less than i. - _R. J. Mathar_, May 15 2013
%F a(n) = Flatten[Join[{{1}}, Table[Reverse[CoefficientList[Product[x - p1[n], {n, 0, m}], x]], {m, 0, 10}]]]
%e 1; # 1
%e 1, -1; # 1-x
%e 1, -2, 1; # (1-x)^2
%e 1, -3, 3, -1; # (1-x)^3
%e 1, -4, 6, -4, 1; # (1-x)^4
%e 1, -5, 10, -10, 5, -1; # (1-x)^5
%e 1, -10, 35, -60, 55, -26, 5; # (1-x)^5*(1-5x)
%e 1, -15, 85, -235, 355, -301, 135, -25; # (1-x)^5*(1-5x)^2
%e 1, -20, 160, -660, 1530, -2076, 1640, -700, 125; # (1-x)^5*(1-5x)^3
%e 1, -25, 260, -1460, 4830, -9726, 12020, -8900, 3625, -625; # (1-x)^5*(1-5x)^4
%e 1, -30, 385, -2760, 12130, -33876, 60650, -69000, 48125, -18750,.. # (1-x)^5*(1-5x)^5
%t a = Join[{{1}}, Table[Reverse[ CoefficientList[Product[x - p1[n], {n, 0, m}], x]], {m, 0, 10}]] aout = Flatten[a]
%Y Cf. A007318, A118686.
%K sign,uned,tabf,obsc
%O 0,5
%A _Roger L. Bagula_ Jun 14 2006
%E Should be edited in the same way that I edited A118686. Unfortunately p1 has not been defined, but must be related to "Mod[(Prime[n] - 1)/2, 4] == 2". Compare the definition of p[n] in A118686. - _N. J. A. Sloane_, Oct 08 2006