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A067410 Triangle with columns built from certain power sequences.

%I A067410 #21 Sep 30 2022 23:30:29
%S A067410 1,2,1,4,3,1,8,12,4,1,16,48,24,5,1,32,192,144,40,6,1,64,768,864,320,
%T A067410 60,7,1,128,3072,5184,2560,600,84,8,1,256,12288,31104,20480,6000,1008,
%U A067410 112,9,1,512,49152,186624,163840,60000,12096,1568,144,10,1
%N A067410 Triangle with columns built from certain power sequences.
%H A067410 Indranil Ghosh, <a href="/A067410/b067410.txt">Rows 0..125, flattened</a>
%F A067410 a(n, m) = 1 if n = m; a(n, m) = (m+2)*(2*(m+1))^(n-m-1) if n > m >= 0.
%F A067410 G.f. for column m: (x^m)*(1-m*x)/(1-2*(m+1)*x).
%e A067410 Triangle starts:
%e A067410   1;
%e A067410   2,  1;
%e A067410   4,  3, 1;
%e A067410   8, 12, 4, 1;
%e A067410   ...
%t A067410 A[n_,m_]:=If[n==m,1,(m+2)(2(m+1))^(n-m-1)]; Flatten[Table[A[n,m],{n,0,9},{m,0,n}]] (* _Stefano Spezia_, Sep 30 2022 *)
%Y A067410 Cf. A009998 (triangle built from powers of (m+1)), A067402.
%Y A067410 Columns m=0..8 are A000079, A002001, A067411, A067412, A090019, A067413, A067414, A067415, A067416.
%K A067410 nonn,easy,tabl
%O A067410 0,2
%A A067410 _Wolfdieter Lang_, Jan 25 2002