A067410 Triangle with columns built from certain power sequences.

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, 60, 7, 1, 128, 3072, 5184, 2560, 600, 84, 8, 1, 256, 12288, 31104, 20480, 6000, 1008, 112, 9, 1, 512, 49152, 186624, 163840, 60000, 12096, 1568, 144, 10, 1

Offset

0,2

Links

Indranil Ghosh, Rows 0..125, flattened

Formula

a(n, m) = 1 if n = m; a(n, m) = (m+2)*(2*(m+1))^(n-m-1) if n > m >= 0.

G.f. for column m: (x^m)*(1-m*x)/(1-2*(m+1)*x).

Example

Triangle starts:
  1;
  2,  1;
  4,  3, 1;
  8, 12, 4, 1;
  ...

Mathematica

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 *)

Crossrefs

Cf. A009998 (triangle built from powers of (m+1)), A067402.

Columns m=0..8 are A000079, A002001, A067411, A067412, A090019, A067413, A067414, A067415, A067416.

Sequence in context: A051129 A319075 A264871 * A213947 A348482 A188403

Adjacent sequences: A067407 A067408 A067409 * A067411 A067412 A067413

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jan 25 2002

Status

approved