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A084602 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1 + x + 3x^2)^n.

%I A084602 #15 Mar 03 2017 02:46:14
%S A084602 1,1,1,3,1,2,7,6,9,1,3,12,19,36,27,27,1,4,18,40,91,120,162,108,81,1,5,
%T A084602 25,70,185,331,555,630,675,405,243,1,6,33,110,330,726,1441,2178,2970,
%U A084602 2970,2673,1458,729,1,7,42,161,539,1386,3157,5797,9471,12474,14553
%N A084602 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1 + x + 3x^2)^n.
%H A084602 G. C. Greubel, <a href="/A084602/b084602.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%e A084602 Rows:
%e A084602 {1},
%e A084602 {1,1, 3},
%e A084602 {1,2, 7,  6,  9},
%e A084602 {1,3,12, 19, 36, 27,  27},
%e A084602 {1,4,18, 40, 91,120, 162, 108,  81},
%e A084602 {1,5,25, 70,185,331, 555, 630, 675, 405, 243},
%e A084602 {1,6,33,110,330,726,1441,2178,2970,2970,2673,1458,729},
%t A084602 With[{eq = (1 + x + 3*x^2)}, Flatten[Table[CoefficientList[Expand[eq^n], x], {n, 0, 10}]]] (* _G. C. Greubel_, Mar 02 2017 *)
%o A084602 (PARI) for(n=0,15, for(k=0,2*n,t=polcoeff((1+x+3*x^2)^n,k,x); print1(t",")); print(" "))
%Y A084602 Cf. A002426, A084600-A084601, A084603-A084615.
%K A084602 nonn,tabf
%O A084602 0,4
%A A084602 _Paul D. Hanna_, Jun 01 2003