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Triangle with columns built from certain power sequences.
5

%I #23 Oct 16 2024 09:22:06

%S 1,4,1,16,5,1,64,40,6,1,256,320,72,7,1,1024,2560,864,112,8,1,4096,

%T 20480,10368,1792,160,9,1,16384,163840,124416,28672,3200,216,10,1,

%U 65536,1310720,1492992,458752,64000

%N Triangle with columns built from certain power sequences.

%C The fifth column (m=4) gives [1, 8, 160, 3200, 64000, 1280000, 25600000, ...].

%H Indranil Ghosh, <a href="/A067425/b067425.txt">Rows 0..125, flattened</a>

%F 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 G.f. for column m: (x^m)*(1-3*m*x)/(1-4*(m+1)*x).

%e Triangle starts:

%e 1;

%e 4, 1;

%e 16, 5, 1;

%e 64, 40, 6, 1;

%e ...

%t A067425[n_, m_] := If[n == m, 1, (m + 4)*(4*(m + 1))^(n - m - 1)];

%t Table[A067425[n, m], {n, 0, 10}, {m, 0, n}] (* _Paolo Xausa_, Oct 16 2024 *)

%Y Cf. A009998, A067410, A067417.

%Y Columns 0..3 are A000302 (powers of 4), A067412, A067419, A067404.

%Y Columns 5..8 are A067426, A067427, A067428, A067429.

%K nonn,easy,tabl

%O 0,2

%A _Wolfdieter Lang_, Jan 25 2002