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A114163 Triangle read by rows, based on a simple Jacobsthal number recursion rule.

%I A114163 #4 Mar 30 2012 18:59:13
%S A114163 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 A114163 1,7,543,2169,3687,1181,85,1,1,8,1636,11388,42726,28488,4836,170,1,1,
%U A114163 9,4916,58576,481374,640974,236436,19286,341,1,1,10,14757,297796,5353690
%N A114163 Triangle read by rows, based on a simple Jacobsthal number recursion rule.
%C A114163 Subdiagonal S(n+1,n) is A000975(n+1). Row sums of inverse are 0^n.
%F A114163 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 A114163 Triangle begins
%e A114163 1....1....3....5...11...21...43....J(k+1)
%e A114163 1
%e A114163 1....1
%e A114163 1....2....1
%e A114163 1....3....5....1
%e A114163 1....4...18...10....1
%e A114163 1....5...58...68...21....1
%e A114163 1....6..179..398..299...42....1
%e A114163 For example, T(6,3)=398=58+5*68=T(5,2)+J(4)*T(5,3).
%Y A114163 Cf. A111669.
%K A114163 easy,nonn,tabl
%O A114163 0,5
%A A114163 _Paul Barry_, Nov 14 2005