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A167565 A triangle related to the a(n) formulas for the rows of the ED2 array A167560.

%I A167565 #6 Jun 16 2016 23:22:58
%S A167565 1,2,0,3,1,2,4,4,16,0,5,10,67,14,24,6,20,202,124,368,0,7,35,497,601,
%T A167565 2736,444,720,8,56,1064,2120,13712,6464,16896,0,9,84,2058,6096,53121,
%U A167565 48876,186732,25584,40320,10,120,3684,15168,171258,257640,1350296
%N A167565 A triangle related to the a(n) formulas for the rows of the ED2 array A167560.
%C A167565 The a(n) formulas given below correspond to the first ten rows of the ED2 array A167560.
%C A167565 The recurrence relations for the a(n) formulas for the left hand triangle columns, see the cross-references below, lead to the sequences A003148 and A007318.
%e A167565 Row 1: a(n) = 1.
%e A167565 Row 2: a(n) = 2*n + 0.
%e A167565 Row 3: a(n) = 3*n^2 + 1*n + 2.
%e A167565 Row 4: a(n) = 4*n^3 + 4*n^2 + 16*n + 0.
%e A167565 Row 5: a(n) = 5*n^4 + 10*n^3 + 67*n^2 + 14*n + 24.
%e A167565 Row 6: a(n) = 6*n^5 + 20*n^4 + 202*n^3 + 124*n^2 + 368*n + 0.
%e A167565 Row 7: a(n) = 7*n^6 + 35*n^5 + 497*n^4 + 601*n^3 + 2736*n^2 + 444*n + 720.
%e A167565 Row 8: a(n) = 8*n^7 + 56*n^6 + 1064*n^5 + 2120*n^4 + 13712*n^3 + 6464*n^2 + 16896*n + 0.
%e A167565 Row 9: a(n) = 9*n^8 + 84*n^7 + 2058*n^6 + 6096*n^5 + 53121*n^4 + 48876*n^3 + 186732*n^2 + 25584*n + 40320.
%e A167565 Row 10: a(n) = 10*n^9 + 120*n^8 + 3684*n^7 + 15168*n^6 + 171258*n^5 + 257640*n^4 + 1350296*n^3 + 533472*n^2 + 1297152*n + 0.
%Y A167565 A167560 is the ED2 array.
%Y A167565 A000012, A005843 (n=>1), 2*A104249 (n=>1), A167561, A167562 and A167563 equal the first sixth rows of the array.
%Y A167565 A005359 equals the first right hand triangle column.
%Y A167565 A000027, A000292, A167566, A167567 and A168304 equal the first five left hand triangle columns.
%Y A167565 A000142 equals the row sums.
%Y A167565 Cf. A003148 and A007318.
%K A167565 nonn,tabl
%O A167565 1,2
%A A167565 _Johannes W. Meijer_, Nov 10 2009
%E A167565 Comment and links added by _Johannes W. Meijer_, Nov 23 2009