# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a167572 Showing 1-1 of 1 %I A167572 #6 Jun 16 2016 23:27:41 %S A167572 1,5,1,23,11,1,167,83,17,1,1473,741,183,23,1,16413,8169,2043,323,29,1, %T A167572 211479,106107,26529,4409,503,35,1,3192975,1592235,398025,66345,8175, %U A167572 723,41,1,54010305,27062325,6765975,1127655,140865,13677,983,47,1 %N A167572 The ED3 array read by antidiagonals %C A167572 The coefficients in the upper right triangle of the ED3 array (m>n) were found with the a(n,m) formula while the coefficients in the lower left triangle of the ED3 array (m<=n) were found with the recurrence relation, see below. We use for the array rows the letter n (>=1) and for the array columns the letter m (>=1). %C A167572 For the ED1, ED2 and ED4 arrays see A167546, A167560 and A167584. %H A167572 Johannes W. Meijer, The four Escher-Droste arrays, jpg image, Mar 08 2013. %F A167572 a(n,m) = ((2*m-1)!!/ (2*m-2*n-1)!!)*int(sinh(y*(2*n-1))/(cosh(y))^(2*m),y=0..infinity) for m>n. %F A167572 The (n-1)-differences of the n-th array row lead to the recurrence relation %F A167572 sum((-1)^k*binomial(n-1,k)*a(n,m-k),k=0..n-1) = 2^(n-1)*(n-1)!*(2*n-1). %e A167572 The ED3 array begins with: %e A167572 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 %e A167572 5, 11, 17, 23, 29, 35, 41, 47, 53, 59 %e A167572 23, 83, 183, 323, 503, 723, 983, 1283, 1623, 2003 %e A167572 167, 741, 2043, 4409, 8175, 13677, 21251, 31233, 43959, 59765 %e A167572 1473, 8169, 26529, 66345, 140865, 266793, 464289, 756969, 1171905, 1739625 %e A167572 16413, 106107, 398025, 1127655, 2678325, 5623443, 10768737, 19194495, 32297805, 51834795 %Y A167572 A000012, A016969, A167573, A167574 and A167575 equal the first five rows of the array. %Y A167572 A167576, A167577 and A167578 equal the first three columns of the array. %Y A167572 A167579 equals the row sums of the ED3 array read by antidiagonals. %Y A167572 A167580 is a triangle related to the a(n) formulas of the rows of the ED3 array. %Y A167572 A167583 is a triangle related to the GF(z) formulas of the rows of the ED3 array. %Y A167572 Cf. A014481 (the 2^(n-1)*(n-1)!*(2*n-1) factor). %Y A167572 Cf. A167546 (ED1 array), A167560 (ED2 array), A167584 (ED4 array). %K A167572 nonn,tabl %O A167572 1,2 %A A167572 _Johannes W. Meijer_, Nov 10 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE