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A176158 Triangle read by rows: T(n,m) = (1 + 2 * binomial(n,m))^n for 0 <= m <= n, n >= 0.

%I A176158 #15 Dec 06 2024 11:11:30
%S A176158 1,3,3,9,25,9,27,343,343,27,81,6561,28561,6561,81,243,161051,4084101,
%T A176158 4084101,161051,243,729,4826809,887503681,4750104241,887503681,
%U A176158 4826809,729,2187,170859375,271818611107,9095120158391,9095120158391,271818611107,170859375,2187
%N A176158 Triangle read by rows: T(n,m) = (1 + 2 * binomial(n,m))^n for 0 <= m <= n, n >= 0.
%C A176158 Row sums are: 1, 6, 43, 740, 41845, 8490790, 6534766679, 18734219262120, 209617607911694569, 8719076076193077820874, 1429879617351180068934959131, ... .
%F A176158 T(n,m) = (1 + 2*binomial(n,m))^n.
%e A176158 {1},
%e A176158 {3, 3},
%e A176158 {9, 25, 9},
%e A176158 {27, 343, 343, 27},
%e A176158 {81, 6561, 28561, 6561, 81},
%e A176158 {243, 161051, 4084101, 4084101, 161051, 243},
%e A176158 {729, 4826809, 887503681, 4750104241, 887503681, 4826809, 729},
%e A176158 {2187, 170859375, 271818611107, 9095120158391, 9095120158391, 271818611107, 170859375, 2187}.
%p A176158 f:= proc(n) local m; seq((binomial(n,m)*2+1)^n, m=0..n) end proc:
%p A176158 for n from 0 to 10 do f(n) od; # _Robert Israel_, Dec 04 2024
%t A176158 Clear[p, n, m];
%t A176158 p[x_, n_, m_] := (1 + 2*Binomial[n, m]*x)^n;
%t A176158 Table[Table[ Apply[Plus, CoefficientList[p[x, n, m], x]], {m, 0, n}], {n, 0, 10}];
%t A176158 Flatten[%]
%Y A176158 Columns m=0-1 give: A000244, A085527.
%K A176158 nonn,tabl
%O A176158 0,2
%A A176158 _Roger L. Bagula_, Apr 10 2010
%E A176158 Edited by _Robert Israel_, Dec 04 2024