%I A088996
%S A088996 1,0,1,0,1,2,0,2,7,6,0,6,29,46,24,0,24,146,329,326,120,0,120,874,2521,
%T A088996 3604,2556,720,0,720,6084,21244,39271,40564,22212,5040,0,5040,48348,
%U A088996 197380,444849,598116,479996,212976,40320
%N A088996 Triangle T(n,k) read by rows, given by [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 
               5, 6, 6, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] where 
               DELTA is the operator defined in A084938.
%C A088996 Diagonals give A000007, A000142; A000142, A067318 . Row sums : A001147 
               . Sum(k=0..n, (-1)^k*T(n,k))= (-1)^n.
%F A088996 E.g.f.: (1-y-y*x)^(-1/(1+x)). Sum(k=0..n, T(n, k)*x^k) = Product(k=1..n, 
               k*x+k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 15 2004
%F A088996 T(n, k) = n*T(n-1, k-1) + (n-1)*T(n-1, k); T(0, 0) = 1, T(0, k) = 0 if 
               k>0, T(n, k) = 0 if k<0. - Philippe DELEHAM, May 22 2005
%F A088996 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A019590(n+1), A000012(n), A000142(n), 
               A001147(n), A007559(n), A007696(n), A008548(n), A008542(n), A045754(n), 
               A045755(n) for x= -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 respectively . Sum_{k, 
               0<=k<=n}T(n,k)*x^k = A033999(n), A000007(n), A001147(n), A008544(n), 
               A008545(n), A008546(n), A008543(n), A049209(n), A049210(n), A049211(n), 
               A049212(n) for x= -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively . 
               - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 10 2007
%e A088996 Triangle begins:
%e A088996 1;
%e A088996 0, 1;
%e A088996 0, 1, 2;
%e A088996 0, 2, 7, 6;
%e A088996 0, 6, 29, 46, 24;
%e A088996 0, 24, 146, 329, 326, 120;
%e A088996 0, 120, 874, 2521, 3604, 2556, 720;
%e A088996 0, 720, 6084, 21244, 39271, 40564, 22212, 5040;
%e A088996 0, 5040, 48348, 197380, 444849, 598116, 479996, 212976, 40320;
%Y A088996 Cf. A000007 A000142 A001147 A067318 A084938.
%Y A088996 Sequence in context: A111111 A161014 A154852 this_sequence A021497 A029593 
               A004514
%Y A088996 Adjacent sequences: A088993 A088994 A088995 this_sequence A088997 A088998 
               A088999
%K A088996 easy,nonn,tabl
%O A088996 0,6
%A A088996 DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 01 2003, Aug 17 2007