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A171824 Triangle T(n,k)= binomial(n + k,n) + binomial(2*n-k,n) read by rows.

%I A171824 #10 Apr 30 2021 02:23:10
%S A171824 2,3,3,7,6,7,21,14,14,21,71,40,30,40,71,253,132,77,77,132,253,925,469,
%T A171824 238,168,238,469,925,3433,1724,828,450,450,828,1724,3433,12871,6444,
%U A171824 3048,1452,990,1452,3048,6444,12871,48621,24320,11495,5225,2717,2717,5225,11495,24320,48621
%N A171824 Triangle T(n,k)= binomial(n + k,n) + binomial(2*n-k,n) read by rows.
%H A171824 G. C. Greubel, <a href="/A171824/b171824.txt">Table of n, a(n) for n = 0..1325</a>
%F A171824 T(n,k) = A046899(n,k) + A092392(n,k).
%F A171824 Sum_{k=0..n} T(n,k) = binomial(2*n+2, n+1) = 2*A001700(n) = A000984(n+1). - _G. C. Greubel_, Apr 29 2021
%e A171824 Triangle begins as:
%e A171824        2;
%e A171824        3,     3;
%e A171824        7,     6,     7;
%e A171824       21,    14,    14,    21;
%e A171824       71,    40,    30,    40,   71;
%e A171824      253,   132,    77,    77,  132,  253;
%e A171824      925,   469,   238,   168,  238,  469, 925;
%e A171824     3433,  1724,   828,   450,  450,  828, 1724,  3433;
%e A171824    12871,  6444,  3048,  1452,  990, 1452, 3048,  6444, 12871;
%e A171824    48621, 24320, 11495,  5225, 2717, 2717, 5225, 11495, 24320, 48621;
%e A171824   184757, 92389, 43824, 19734, 9009, 6006, 9009, 19734, 43824, 92389, 184757;
%t A171824 T[n_, k_] = Binomial[n+k, k] + Binomial[2*n-k, n-k];
%t A171824 Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten
%o A171824 (Magma)
%o A171824 T:= func< n,k | Binomial(n+k,n) + Binomial(2*n-k,n) >;
%o A171824 [T(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Apr 29 2021
%o A171824 (Sage)
%o A171824 def T(n, k): return binomial(n+k,n) + binomial(2*n-k,n)
%o A171824 flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Apr 29 2021
%Y A171824 Row sums are A000984(n+1).
%Y A171824 Cf. A001700, A007318, A054142, A085478.
%K A171824 nonn,tabl,easy
%O A171824 0,1
%A A171824 _Roger L. Bagula_, Dec 19 2009
%E A171824 Formula and row sums reference added by the Assoc. Editors of the OEIS, Feb 24 2010