A067402 - OEIS

%I #21 Sep 30 2022 09:57:05

%S 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,

%T 225,11,1,1,3072,32805,28672,5625,396,13,1,1,12288,295245,458752,

%U 140625,14256,637,15,1,1,49152,2657205,7340032,3515625,513216,31213,960,17,1

%N Triangle with columns built from certain power sequences.

%H Indranil Ghosh, <a href="/A067402/b067402.txt">Rows 0..125, flattened</a>

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

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

%e Triangle starts:

%e       m=0   1   2   3   4

%e   n=0:  1;

%e   n=1:  1,  1;

%e   n=2:  1,  3,  1;

%e   n=3:  1, 12,  5,  1;

%e   n=4:  1, 48, 45,  7,  1;

%e   ...

%t 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 *)

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

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

%K nonn,easy,tabl

%O 0,5

%A _Wolfdieter Lang_, Jan 25 2002

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