login
A067402
Triangle with columns built from certain power sequences.
10
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
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