A127501 - OEIS

%I #8 Sep 08 2013 13:31:03

%S 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 11,1,393,897,972,645,279,78,13,1,1107,2727,3273,2475,1269,447,105,15,

%U 1,3139,8272,10835,9136,5369,2254,671,136,17,1

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

%C 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 T(n+1,1)=A055217(n) . Sum_{k, 0<=k<=n}T(n,k)*x^k = A033999(n), A005043(n), A002426(n), A112657(n) for x = -2, -1, 0, 1 respectively.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 3, 3, 1;

%e 7, 10, 5, 1;

%e 19, 31, 21, 7, 1;

%e 51, 96, 79, 36, 9, 1;

%e 141, 294, 282, 159, 55, 11, 1;

%e 393, 897, 972, 645, 279, 78, 13, 1;

%e 1107, 2727, 3273, 2475, 1269, 447, 105, 15, 1;

%e 3139, 8272, 10835, 9136, 5369, 2254, 671, 136, 17, 1; ...

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Apr 01 2007