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Triangle read by rows, based on a simple Jacobsthal number recursion rule.
0

%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