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

0,2

Comments

The column sequences (without leading 0's) give: A000302 (powers of 4), A067412, A067419 and A067404 for m=0..3; A067426-9 for m=5..8. The fifth column (m=4) gives [1, 8, 160, 3200, 64000, 1280000, 25600000, ...].

Links

Indranil Ghosh, Rows 0..125, flattened

Formula

a(n, m) = 1 if n=m; a(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).

Example

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

Crossrefs

Cf. A009998, A067410, A067417.

Sequence in context: A187926 A285281 A285267 * A188481 A138681 A038231

Adjacent sequences: A067422 A067423 A067424 * A067426 A067427 A067428

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jan 25 2002

Status

approved