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A274883 Triangle read by rows, T(n,k) = 2^k*binomial(n,k)*A057977(n-k) for n>=0 and 0<=k<=n.

%I A274883 #12 Jul 14 2016 10:40:03
%S A274883 1,1,2,1,4,4,3,6,12,8,2,24,24,32,16,10,20,120,80,80,32,5,120,120,480,
%T A274883 240,192,64,35,70,840,560,1680,672,448,128,14,560,560,4480,2240,5376,
%U A274883 1792,1024,256,126,252,5040,3360,20160,8064,16128,4608,2304,512
%N A274883 Triangle read by rows, T(n,k) = 2^k*binomial(n,k)*A057977(n-k) for n>=0 and 0<=k<=n.
%e A274883 Triangle starts:
%e A274883                        1;
%e A274883                       1, 2;
%e A274883                     1, 4, 4;
%e A274883                   3, 6, 12, 8;
%e A274883                2, 24, 24, 32, 16;
%e A274883             10, 20, 120, 80, 80, 32;
%e A274883          5, 120, 120, 480, 240, 192, 64;
%e A274883      35, 70, 840, 560, 1680, 672, 448, 128;
%e A274883 14, 560, 560, 4480, 2240, 5376, 1792, 1024, 256;
%p A274883 T := (n,k) -> 2^k*binomial(n,k)*((n-k)!/floor((n-k)/2)!^2)/(floor((n-k)/2)+1);
%p A274883 seq(seq(T(n,k), k=0..n), n=0..9);
%Y A274883 Cf. A000079 (T(n,n)), A057977 (T(n,0)), A077587 (row sum).
%Y A274883 Cf. A189912. Row reversed A091894 is a subtriangle.
%K A274883 nonn,tabl
%O A274883 0,3
%A A274883 _Peter Luschny_, Jul 14 2016