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%I #26 Sep 08 2022 08:45:30
%S 1,7,1,7,14,1,7,21,21,1,7,28,42,28,1,7,35,70,70,35,1,7,42,105,140,105,
%T 42,1,7,49,147,245,245,147,49,1,7,56,196,392,490,392,196,56,1,7,63,
%U 252,588,882,882,588,252,63,1,7,70,315,840,1470,1764,1470,840,315,70,1
%N Triangle read by rows: T(n,k) = 7*binomial(n,k) for 1 <= k <= n with T(n,n) = 1 for n >= 0.
%C Row sums give A048489.
%C Non-diagonal entries of Pascal's triangle are multiplied by 7. - _Emeric Deutsch_, Jun 20 2007
%C The matrix inverse starts
%C 1;
%C -7, 1;
%C 91, -14, 1;
%C -1771, 273, -21, 1;
%C 45955, -7084, 546, -28, 1;
%C -1490587, 229775, -17710, 910, -35, 1;
%C 58018051, -8943522, 689325, -35420, 1365, -42, 1;
%C -2634606331, 406126357, -31302327, 1608425, -61985, 1911, -49, 1;
%C ... - _R. J. Mathar_, Mar 15 2013
%H G. C. Greubel, <a href="/A131115/b131115.txt">Rows n = 0..100 of triangle, flattened</a>
%F G.f.: (1 + 6*x - t*x)/((1-t*x)*(1-x-t*x)). - _Emeric Deutsch_, Jun 20 2007
%e Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
%e 1;
%e 7, 1;
%e 7, 14, 1;
%e 7, 21, 21, 1;
%e 7, 28, 42, 28, 1;
%e 7, 35, 70, 70, 35, 1;
%e ...
%p T := proc (n, k) if k < n then 7*binomial(n, k) elif k = n then 1 else 0 end if end proc; for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - _Emeric Deutsch_, Jun 20 2007
%t Table[If[k==n, 1, 7*Binomial[n, k]], {n,0,10}, {k,0,n}]//Flatten (* _G. C. Greubel_, Nov 18 2019 *)
%o (PARI) T(n,k)=if(k==n,1,7*binomial(n,k)) \\ _Charles R Greathouse IV_, Jan 16 2012
%o (Magma) [k eq n select 1 else 7*Binomial(n,k): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Nov 18 2019
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (k==n): return 1
%o else: return 7*binomial(n, k)
%o [[T(n, k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Nov 18 2019
%o (GAP)
%o T:= function(n,k)
%o if k=n then return 1;
%o else return 7*Binomial(n,k);
%o fi; end;
%o Flat(List([0..10], n-> List([0..n], k-> T(n,k) ))); # _G. C. Greubel_, Nov 18 2019
%Y Cf. A007318, A048489, A131110, A131111, A131112, A131113, A131114.
%K nonn,tabl,easy,less
%O 0,2
%A _Gary W. Adamson_, Jun 15 2007
%E Corrected and extended by _Emeric Deutsch_, Jun 20 2007
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