A067417 Triangle with columns built from certain power sequences.

1, 3, 1, 9, 4, 1, 27, 24, 5, 1, 81, 144, 45, 6, 1, 243, 864, 405, 72, 7, 1, 729, 5184, 3645, 864, 105, 8, 1, 2187, 31104, 32805, 10368, 1575, 144, 9, 1, 6561, 186624, 295245, 124416, 23625, 2592, 189, 10, 1, 19683, 1119744, 2657205, 1492992, 354375, 46656, 3969, 240, 11, 1

Offset

0,2

Links

Indranil Ghosh, Rows 0..125, flattened

Formula

a(n, m) = 1 if n = m; a(n, m) = (m+3)*(3*(m+1))^(n-m-1) if n > m >= 0.

G.f. for column m: (x^m)*(1-2*m*x)/(1-3*(m+1)*x).

Example

Triangle starts:
   1;
   3,  1;
   9,  4, 1;
  27, 24, 5, 1;
  ...

Mathematica

A[n_, m_]:=If[n==m, 1, (m+3)(3(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, A067410.

Columns m=0..8 are A000244, A067411, A067403, A067419, A067420, A067421, A067422, A067423, A067424.

Sequence in context: A140071 A285280 A285266 * A187887 A016577 A308704

Adjacent sequences: A067414 A067415 A067416 * A067418 A067419 A067420

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jan 25 2002

Status

approved