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A131065 Triangle read by rows: T(n,k) = 6*binomial(n,k) - 5 for 0 <= k <= n.

%I A131065 #22 Sep 08 2022 08:45:30
%S A131065 1,1,1,1,7,1,1,13,13,1,1,19,31,19,1,1,25,55,55,25,1,1,31,85,115,85,31,
%T A131065 1,1,37,121,205,205,121,37,1,1,43,163,331,415,331,163,43,1,1,49,211,
%U A131065 499,751,751,499,211,49,1,1,55,265,715,1255,1507,1255,715,265,55,1
%N A131065 Triangle read by rows: T(n,k) = 6*binomial(n,k) - 5 for 0 <= k <= n.
%C A131065 Row sums = A131066.
%C A131065 The matrix inverse starts:
%C A131065        1;
%C A131065       -1,       1;
%C A131065        6,      -7,      1;
%C A131065      -66,      78,    -13,      1;
%C A131065     1086,   -1284,    216,    -19,   1;
%C A131065   -23826,   28170,  -4740,    420, -25,   1;
%C A131065   653406, -772536, 129990, -11520, 690, -31, 1; - _R. J. Mathar_, Mar 12 2013
%H A131065 Indranil Ghosh, <a href="/A131065/b131065.txt">Rows 0..120 of triangle, flattened</a>
%F A131065 G.f.: (1-z-t*z+6*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - _Emeric Deutsch_, Jun 20 2007
%e A131065 First few rows of the triangle are:
%e A131065   1;
%e A131065   1,  1;
%e A131065   1,  7,  1;
%e A131065   1, 13, 13,  1;
%e A131065   1, 19, 31, 19,  1;
%e A131065   1, 25, 55, 55, 25, 1;
%e A131065 ...
%p A131065 T := proc (n, k) if k <= n then 6*binomial(n, k)-5 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # _Emeric Deutsch_, Jun 20 2007
%t A131065 Table[6*Binomial[n,k]-5,{n,0,15},{k,0,n}]//Flatten (* _Harvey P. Dale_, May 15 2016 *)
%o A131065 (Magma) [6*Binomial(n,k) -5: k in [0..n], n in [0..10]]; // _G. C. Greubel_, Mar 12 2020
%o A131065 (Sage) [[6*binomial(n,k) -5 for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Mar 12 2020
%Y A131065 Cf. A109128, A123203, A131060, A131061, A131063, A131064, A131066, A131067, A131068.
%K A131065 nonn,tabl
%O A131065 0,5
%A A131065 _Gary W. Adamson_, Jun 13 2007
%E A131065 More terms from _Emeric Deutsch_, Jun 20 2007