%I #4 Mar 30 2012 18:59:13
%S 1,1,1,1,2,1,1,3,5,1,1,4,18,10,1,1,5,58,68,21,1,1,6,179,398,299,42,1,
%T 1,7,543,2169,3687,1181,85,1,1,8,1636,11388,42726,28488,4836,170,1,1,
%U 9,4916,58576,481374,640974,236436,19286,341,1,1,10,14757,297796,5353690
%N Triangle read by rows, based on a simple Jacobsthal number recursion rule.
%C Subdiagonal S(n+1,n) is A000975(n+1). Row sums of inverse are 0^n.
%F Number triangle T(n, k)=T(n-1, k-1)+J(k+1)*T(n-1, k) where J(n)=A001045(n); Column k has g.f. x^k/Product(1-J(i+1)x, i, 0, k).
%e Triangle begins
%e 1....1....3....5...11...21...43....J(k+1)
%e 1
%e 1....1
%e 1....2....1
%e 1....3....5....1
%e 1....4...18...10....1
%e 1....5...58...68...21....1
%e 1....6..179..398..299...42....1
%e For example, T(6,3)=398=58+5*68=T(5,2)+J(4)*T(5,3).
%Y Cf. A111669.
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Nov 14 2005