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A067417 Triangle with columns built from certain power sequences.

%I A067417 #26 Sep 30 2022 23:32:24
%S A067417 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 A067417 864,105,8,1,2187,31104,32805,10368,1575,144,9,1,6561,186624,295245,
%U A067417 124416,23625,2592,189,10,1,19683,1119744,2657205,1492992,354375,46656,3969,240,11,1
%N A067417 Triangle with columns built from certain power sequences.
%H A067417 Indranil Ghosh, <a href="/A067417/b067417.txt">Rows 0..125, flattened</a>
%F A067417 a(n, m) = 1 if n = m; a(n, m) = (m+3)*(3*(m+1))^(n-m-1) if n > m >= 0.
%F A067417 G.f. for column m: (x^m)*(1-2*m*x)/(1-3*(m+1)*x).
%e A067417 Triangle starts:
%e A067417    1;
%e A067417    3,  1;
%e A067417    9,  4, 1;
%e A067417   27, 24, 5, 1;
%e A067417   ...
%t A067417 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 A067417 Cf. A009998 (triangle built from powers of (m+1)), A067402, A067410.
%Y A067417 Columns m=0..8 are A000244, A067411, A067403, A067419, A067420, A067421, A067422, A067423, A067424.
%K A067417 nonn,easy,tabl
%O A067417 0,2
%A A067417 _Wolfdieter Lang_, Jan 25 2002