A067402 Triangle with columns built from certain power sequences.

1, 1, 1, 1, 3, 1, 1, 12, 5, 1, 1, 48, 45, 7, 1, 1, 192, 405, 112, 9, 1, 1, 768, 3645, 1792, 225, 11, 1, 1, 3072, 32805, 28672, 5625, 396, 13, 1, 1, 12288, 295245, 458752, 140625, 14256, 637, 15, 1, 1, 49152, 2657205, 7340032, 3515625, 513216, 31213, 960, 17, 1

Offset

0,5

Links

Indranil Ghosh, Rows 0..125, flattened

Formula

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

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

Example

Triangle starts:
      m=0   1   2   3   4
  n=0:  1;
  n=1:  1,  1;
  n=2:  1,  3,  1;
  n=3:  1, 12,  5,  1;
  n=4:  1, 48, 45,  7,  1;
  ...

Mathematica

A[n_, m_]:=If[n==m, 1, (2m+1)(m+1)^(2(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)).

Columns m=0..8: A000012, A002001, A067403-A067409.

Sequence in context: A168552 A111473 A234944 * A113340 A134523 A098778

Adjacent sequences: A067399 A067400 A067401 * A067403 A067404 A067405

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jan 25 2002

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002

Status

approved