A067425 Triangle with columns built from certain power sequences.

1, 4, 1, 16, 5, 1, 64, 40, 6, 1, 256, 320, 72, 7, 1, 1024, 2560, 864, 112, 8, 1, 4096, 20480, 10368, 1792, 160, 9, 1, 16384, 163840, 124416, 28672, 3200, 216, 10, 1, 65536, 1310720, 1492992, 458752, 64000

Offset: 0

Author

Wolfdieter Lang, Jan 25 2002

Keywords

• nonn
• easy
• tabl

Comments

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

Examples

			Triangle starts:
   1;
   4,  1;
  16,  5,  1;
  64, 40,  6,  1;
  ...
		

Links

• Indranil Ghosh, Rows 0..125, flattened

Crossrefs

Cf. A009998, A067410, A067417.

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

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

Programs

Mathematica

A067425[n_, m_] := If[n == m, 1, (m + 4)*(4*(m + 1))^(n - m - 1)];
Table[A067425[n, m], {n, 0, 10}, {m, 0, n}] (* Paolo Xausa, Oct 16 2024 *)

Formula

T(n,m) = 1 if n = m; T(n,m) = (m+4)*(4*(m+1))^(n-m-1) if n > m >= 0, else 0.

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