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
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
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