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A177977 Triangle read by rows. Polynomials based on sums of Moebius transforms.

%I A177977 #3 May 01 2013 21:08:58
%S A177977 1,1,0,1,3,-2,1,6,5,-6,1,10,35,26,-48,1,15,85,165,-26,-120,1,21,175,
%T A177977 735,1264,-36,-1440,1,28,322,1960,5929,8092,-1212,-10080,1,36,546,
%U A177977 4536,22449,60564,57644,-24816,-80640,1,45,870,9450,63273,254205,572480
%N A177977 Triangle read by rows. Polynomials based on sums of Moebius transforms.
%C A177977 These polynomials were found by entering the rows of A177976 in Wolfram Alpha. The lower left half equals part of the Stirling numbers of the first kind given in table A094638. To evaluate, enter a value for n and divide row sums with factorial numbers as shown in the example section. n=-1 gives A092149, n=0 gives the Mertens function A002321, n=1 gives A000012, n=2 gives A002088, n=3 gives A015631, and n=4 gives A015634.
%e A177977 Triangle begins and the polynomials are:
%e A177977 (1*n^0)/1
%e A177977 (1*n^1 +0*n^0)/1
%e A177977 (1*n^2 +3*n^1 -2*n^0)/2
%e A177977 (1*n^3 +6*n^2 +5*n^1 -6*n^0)/6
%e A177977 (1*n^4 +10*n^3 +35*n^2 +26*n^1 -48*n^0)/24
%e A177977 (1*n^5 +15*n^4 +85*n^3 +165*n^2 -26*n^1 -120*n^0)/120
%e A177977 (1*n^6 +21*n^5 +175*n^4 +735*n^3 +1264*n^2 -36*n^1 -1440*n^0)/720
%K A177977 sign,tabl
%O A177977 1,5
%A A177977 _Mats Granvik_, May 16 2010
%E A177977 Typo in sequence (erroneous comma) corrected by _N. J. A. Sloane_, May 22 2010