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A067425 Triangle with columns built from certain power sequences.

%I A067425 #23 Oct 16 2024 09:22:06
%S A067425 1,4,1,16,5,1,64,40,6,1,256,320,72,7,1,1024,2560,864,112,8,1,4096,
%T A067425 20480,10368,1792,160,9,1,16384,163840,124416,28672,3200,216,10,1,
%U A067425 65536,1310720,1492992,458752,64000
%N A067425 Triangle with columns built from certain power sequences.
%C A067425 The fifth column (m=4) gives [1, 8, 160, 3200, 64000, 1280000, 25600000, ...].
%H A067425 Indranil Ghosh, <a href="/A067425/b067425.txt">Rows 0..125, flattened</a>
%F A067425 T(n,m) = 1 if n = m; T(n,m) = (m+4)*(4*(m+1))^(n-m-1) if n > m >= 0, else 0.
%F A067425 G.f. for column m: (x^m)*(1-3*m*x)/(1-4*(m+1)*x).
%e A067425 Triangle starts:
%e A067425    1;
%e A067425    4,  1;
%e A067425   16,  5,  1;
%e A067425   64, 40,  6,  1;
%e A067425   ...
%t A067425 A067425[n_, m_] := If[n == m, 1, (m + 4)*(4*(m + 1))^(n - m - 1)];
%t A067425 Table[A067425[n, m], {n, 0, 10}, {m, 0, n}] (* _Paolo Xausa_, Oct 16 2024 *)
%Y A067425 Cf. A009998, A067410, A067417.
%Y A067425 Columns 0..3 are A000302 (powers of 4), A067412, A067419, A067404.
%Y A067425 Columns 5..8 are A067426, A067427, A067428, A067429.
%K A067425 nonn,easy,tabl
%O A067425 0,2
%A A067425 _Wolfdieter Lang_, Jan 25 2002