Search: id:A086810
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%I A086810
%S A086810 1,0,1,0,1,2,0,1,5,5,0,1,9,21,14,0,1,14,56,84,42,0,1,20,120,300,330,132,
%T A086810 0,1,27,225,825,1485,1287,429,0,1,35,385,1925,5005,7007,5005,1430,0,1,
%U A086810 44,616,4004,14014,28028,32032,19448,4862,0,1,54,936,7644,34498,91728
%N A086810 Triangle obtained by adding a leading diagonal 1,0,0,0,... to A033282.
%C A086810 Mirror image of triangle A133336 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Dec 10 2008]
%F A086810 Triangle T(n, k) read by rows; given by [0, 1, 0, 1, 0, 1, ...] DELTA 
               [1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is Deleham's operator 
               defined in A084938.
%F A086810 For k>0, T(n, k) = binomial(n+k-1, n)*binomial(n+2k, k)/(n+k+1); T(0, 
               0) = 1 and T(n, 0) = 0 if n>0.
%F A086810 Sum_{k>=0} T(n, k)*2^k = A107841(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               May 26 2005
%F A086810 Sum_{ k>=0} T(n-k, k) = A005043(n) . - Philippe DELEHAM, May 30 2005
%F A086810 T(n, k) = A108263(n+k, k) . - Philippe DELEHAM, May 30 2005
%F A086810 Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A001003(n), A107841(n), A131763(n), 
               A131765(n), A131846(n), A131926(n), A131869(n), A131927(n) for x 
               = 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 05 2007
%F A086810 Sum_{k, 0<=k<=n}T(n,k)*5^k*(-2)^(n-k) = A152601(n). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Dec 10 2008]
%F A086810 Sum_{k, 0<=k<=n}T(n,k)*(-1)^k*3^(n-k) = A154825(n). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Jan 17 2009]
%e A086810 1; 0, 1; 0, 1, 2; 0, 1, 5, 5; 0, 1, 9, 21, 14; ...
%Y A086810 Diagonals : A000007, A000012, A000096, A033275, A033276, A033277, A033278, 
               A033279, A000108, A002054, A002055, A002056, A007160, A033280, A033281
%Y A086810 The diagonals (except for A000007) are also the diagonals of A033282.
%Y A086810 Row sums : A001003 (Schroeder numbers)
%Y A086810 Cf. A033282, A084938.
%Y A086810 Sequence in context: A004483 A085650 A109450 this_sequence A085838 A094456 
               A010028
%Y A086810 Adjacent sequences: A086807 A086808 A086809 this_sequence A086811 A086812 
               A086813
%K A086810 easy,nonn,tabl
%O A086810 0,6
%A A086810 DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 05 2003

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