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

Author

Wolfdieter Lang, Jan 25 2002

Keywords

• nonn
• easy
• tabl

Examples

			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;
  ...
		

Links

• Indranil Ghosh, Rows 0..125, flattened

Crossrefs

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

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

Programs

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 *)

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).

Extensions

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