|
%I #7 Jun 17 2016 02:03:30
%S 1,4,-2,12,-8,9,32,-16,120,-60,80,0,952,-768,525,192,160,5664,-5008,
%T 12396,-5670,448,896,27888,-20672,162740,-133128,72765,1024,3584,
%U 120064,-46720,1537216,-1562464,2557296,-1081080,2304,12288,467712,76800
%N A triangle related to the a(n) formulas of the rows of the ED4 array A167584.
%C The a(n) formulas given below correspond to the first ten rows of the ED4 array A167584.
%C The recurrence relations of the a(n) formulas for the left hand triangle columns, see the cross-references below, lead to the sequences A013609, A003148, A081277 and A079628.
%e Row 1: a(n) = 1.
%e Row 2: a(n) = 4*n - 2.
%e Row 3: a(n) = 12*n^2 - 8*n + 9.
%e Row 4: a(n) = 32*n^3 - 16*n^2 + 120*n - 60.
%e Row 5: a(n) = 80*n^4 + 0*n^3 + 952*n^2 - 768*n + 525.
%e Row 6: a(n) = 192*n^5 + 160*n^4 + 5664*n^3 - 5008*n^2 + 12396*n - 5670.
%e Row 7: a(n) = 448*n^6 + 896*n^5 + 27888*n^4 - 20672*n^3 + 162740*n^2 - 133128*n + 72765.
%e Row 8: a(n) = 1024*n^7 + 3584*n^6 + 120064*n^5 - 46720*n^4 + 1537216*n^3 - 1562464*n^2 + 2557296*n - 1081080.
%e Row 9: a(n) = 2304*n^8 + 12288*n^7 + 467712*n^6 + 76800*n^5 + 11589216*n^4 - 12058368*n^3 + 47963568*n^2 - 38278080*n + 18243225.
%e Row 10: a(n) = 5120*n^9 + 38400*n^8 + 1686528*n^7 + 1540608*n^6 + 73898880*n^5 - 66179520*n^4 + 631348672*n^3 - 669559008*n^2 + 869709780*n - 344594250.
%Y A167584 is the ED4 array.
%Y A000012, A016825, A167585, A167586 and A167587 equal the first five rows of the ED4 array.
%Y A001787, A167592, A167593, A168307 and A168308 equal the first five left hand triangle columns.
%Y A001193 equals the first right hand triangle column.
%Y A024199 equals the row sums.
%Y Cf. A013609, A003148, A079628 and A081277.
%K sign,tabl
%O 1,2
%A _Johannes W. Meijer_, Nov 10 2009
%E Comment and formulas added by _Johannes W. Meijer_, Nov 23 2009
| 