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A127501 Triangle read by rows :T(n,k)=Sum_{j, j>=0}A089942(n,j)*binomial(j,k).

%I A127501 #11 Mar 16 2025 02:35:17
%S A127501 1,1,1,3,3,1,7,10,5,1,19,31,21,7,1,51,96,79,36,9,1,141,294,282,159,55,
%T A127501 11,1,393,897,972,645,279,78,13,1,1107,2727,3273,2475,1269,447,105,15,
%U A127501 1,3139,8272,10835,9136,5369,2254,671,136,17,1
%N A127501 Triangle read by rows :T(n,k)=Sum_{j, j>=0}A089942(n,j)*binomial(j,k).
%C A127501 Riordan array (1/sqrt(1-2*x-3*x^2), (1+x-sqrt(1-2*x-3*x^2))/(2*sqrt(1-2*x-3*x^2))). - _Philippe Deléham_, Mar 06 2013
%F A127501 T(n+1,1) = A055217(n).
%F A127501 Sum_{k=0..n} T(n,k)*x^k = A033999(n), A005043(n), A002426(n), A112657(n) for x = -2, -1, 0, 1 respectively.
%e A127501 Triangle begins:
%e A127501   1;
%e A127501   1, 1;
%e A127501   3, 3, 1;
%e A127501   7, 10, 5, 1;
%e A127501   19, 31, 21, 7, 1;
%e A127501   51, 96, 79, 36, 9, 1;
%e A127501   141, 294, 282, 159, 55, 11, 1;
%e A127501   393, 897, 972, 645, 279, 78, 13, 1;
%e A127501   1107, 2727, 3273, 2475, 1269, 447, 105, 15, 1;
%e A127501   3139, 8272, 10835, 9136, 5369, 2254, 671, 136, 17, 1; ...
%K A127501 nonn,tabl
%O A127501 0,4
%A A127501 _Philippe Deléham_, Apr 01 2007