|
%I #20 Dec 26 2023 10:07:00
%S 1,4,1,16,7,1,64,38,10,1,256,187,69,13,1,1024,874,406,109,16,1,4096,
%T 3958,2186,748,158,19,1,16384,17548,11124,4570,1240,216,22,1,65536,
%U 76627,54445,25879,8485,1909,283,25,1,262144,330818,259006,138917,52984,14471,2782,359,28,1
%N Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/(2*sqrt(1-4x))).
%C Row sums = A141223;
%C Diagonal sums = A188482;
%C Inverse matrix: (1/(1+2x)^2, x(1+x)/(1+2x)^2).
%F T(n,k) = [x^n] ((1-sqrt(1-4*x))/(2*sqrt(1-4*x))^k/(1-4*x).
%F Recurrence: T(n+1,k+1) = T(n,k) + 3*T(n,k-1) + T(n,k-2) - T(n,k-3) + T(n,k-4) - T(n,k-5) + ...
%e Triangle begins:
%e 1;
%e 4, 1;
%e 16, 7, 1;
%e 64, 38, 10, 1;
%e 256, 187, 69, 13, 1;
%e 1024, 874, 406, 109, 16, 1;
%e 4096, 3958, 2186, 748, 158, 19, 1;
%e 16384, 17548, 11124, 4570, 1240, 216, 22, 1;
%e 65536, 76627, 54445, 25879, 8485, 1909, 283, 25, 1;
%t Flatten[Table[Sum[Binomial[n+i,n]Binomial[n-i,k]2^(n-k-i),{i,0,n-k}],{n,0,8},{k,0,8}]]
%o (Maxima) create_list(sum(binomial(n+i,n)*binomial(n-i,k)*2^(n-k-i),i,0,n-k),n,0,8,k,0,n);
%Y Cf. A141223, A188482.
%K nonn,easy,tabl
%O 0,2
%A _Emanuele Munarini_, Apr 01 2011
%E Comment corrected by _Philippe Deléham_, Jan 22 2014
|
