cp's OEIS Frontend

A211399 Triangle T(n,k), 0 <= k <= n, given by (0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...) DELTA (1, 0, 3, 0, 5, 0, 7, 0, 9, 0, ...) where DELTA is the operator defined in A084938.

%I A211399 #17 Feb 22 2013 14:40:36
%S A211399 1,0,1,0,1,1,0,1,5,1,0,1,15,18,1,0,1,37,129,58,1,0,1,83,646,877,179,1,
%T A211399 0,1,177,2685,8030,5280,543,1,0,1,367,10002,56285,82610,29658,1636,1,
%U A211399 0,1,749,34777,335162
%N A211399 Triangle T(n,k), 0 <= k <= n, given by (0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...) DELTA (1, 0, 3, 0, 5, 0, 7, 0, 9, 0, ...) where DELTA is the operator defined in A084938.
%C A211399 Contains A156920 as submatrix.
%C A211399 Row-reversal of A102365. - _Philippe Deléham_, Feb 12 2013
%F A211399 T(n,k) = k*T(n-1,k) + (2n-2k+1)*T(n-1,k-1) , T(n,n) = 1, T(n,k) = 0 if k<0 or if k>n.
%F A211399 T(n,k) = A185411(n,k)/(2^(n-k)).
%F A211399 Sum_{k, 0<=k<=n} T(n,k)*x^(n-k) = A000012(n), A014307(n), A001147(n) for x = 0, 1, 2 respectively .
%F A211399 G.f.: 1/(1-xy/(1-x/(1-3xy/(1-2x/(1-5xy/(1-3x/(1-7xy/(1- ...(continued fraction).
%e A211399 Triangle begins :
%e A211399 1
%e A211399 0, 1
%e A211399 0, 1, 1
%e A211399 0, 1, 5, 1
%e A211399 0, 1, 15, 18, 1
%e A211399 0, 1, 37, 129, 58, 1
%e A211399 0, 1, 83, 646, 877, 179, 1
%Y A211399 Left hand column sequences: A000007, A000012, A050488, A142965, A142966, A142968.
%Y A211399 Right hand column sequences: A000340, A156922, A156923, A156924.
%Y A211399 Row sums A014307(n).
%K A211399 easy,nonn,tabl
%O A211399 0,9
%A A211399 _Philippe Deléham_, Feb 08 2013