%I A098494
%S A098494 1,1,1,1,5,4,1,12,35,30,1,22,143,362,312,1,35,405,2065,4814,4200,1,51,
%T A098494 925,7965,35434,78744,69120,1,70,1834,24010,173929,709240,1525236,
%U A098494 1345680,1,92,3290,61040,655529,4235588,16255420
%V A098494 1,1,-1,1,-5,4,1,-12,35,-30,1,-22,143,-362,312,1,-35,405,-2065,4814,-4200,
               1,-51,925,
%W A098494 -7965,35434,-78744,69120,1,-70,1834,-24010,173929,-709240,1525236,-1345680,
               1,-92,3290,
%X A098494 -61040,655529,-4235588,16255420
%N A098494 Triangle read by rows: coefficients of polynomials E(n,x) related to 
               partitions with parts occurring at most thrice.
%C A098494 The polynomials generate (-1)^k*n! times the diagonals of A098493.
%D A098494 A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring 
               at most thrice, in preparation.
%e A098494 E(0,x) = 1
%e A098494 E(1,x) = x - 1
%e A098494 E(2,x) = x^2 - 5*x + 4
%e A098494 E(3,x) = x^3 - 12*x^2 + 35*x - 30
%e A098494 E(4,x) = x^4 - 22*x^3 + 143*x^2 - 362*x + 312
%e A098494 E(5,x) = x^5 - 35*x^4 + 405*x^3 - 2065*x^2 + 4814*x - 4200
%Y A098494 Columns include -A000326. Constant terms E(n, 0) = -E(n-1, -1) = n!/2*A085455 
               = (-1)^n*n!*A005773. Row sums are E(n, 1) = (-1)^n*n!*A005774.
%Y A098494 Sequence in context: A011503 A072222 A005752 this_sequence A008955 A152862 
               A108440
%Y A098494 Adjacent sequences: A098491 A098492 A098493 this_sequence A098495 A098496 
               A098497
%K A098494 sign,tabl
%O A098494 0,5
%A A098494 Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2004