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Triangle with columns built from certain power sequences.
10

%I #26 Sep 30 2022 23:32:24

%S 1,3,1,9,4,1,27,24,5,1,81,144,45,6,1,243,864,405,72,7,1,729,5184,3645,

%T 864,105,8,1,2187,31104,32805,10368,1575,144,9,1,6561,186624,295245,

%U 124416,23625,2592,189,10,1,19683,1119744,2657205,1492992,354375,46656,3969,240,11,1

%N Triangle with columns built from certain power sequences.

%H Indranil Ghosh, <a href="/A067417/b067417.txt">Rows 0..125, flattened</a>

%F a(n, m) = 1 if n = m; a(n, m) = (m+3)*(3*(m+1))^(n-m-1) if n > m >= 0.

%F G.f. for column m: (x^m)*(1-2*m*x)/(1-3*(m+1)*x).

%e Triangle starts:

%e 1;

%e 3, 1;

%e 9, 4, 1;

%e 27, 24, 5, 1;

%e ...

%t A[n_,m_]:=If[n==m,1,(m+3)(3(m+1))^(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)), A067402, A067410.

%Y Columns m=0..8 are A000244, A067411, A067403, A067419, A067420, A067421, A067422, A067423, A067424.

%K nonn,easy,tabl

%O 0,2

%A _Wolfdieter Lang_, Jan 25 2002