%I A008301
%S A008301 1,1,2,1,4,8,10,8,4,34,68,94,104,94,68,34,496,992,1420,1712,1816,1712,
%T A008301 1420,992,496,11056,22112,32176,40256,45496,47312,45496,40256,32176,
%U A008301 22112,11056,349504,699008,1026400,1309568,1528384,1666688,1714000
%N A008301 Poupard's triangle: triangle of numbers arising in enumeration of binary 
               trees.
%D A008301 C. Poupard, Deux proprietes des arbres binaires ordonnes stricts, European 
               J. Combin., 10 (1989), 369-374.
%D A008301 Dominique Foata and Guo-Niu Han, Dimers and new q-tangent numbers, Preprint, 
               2008.
%D A008301 Dominique Foata and Guo-Niu Han, The dimer polynomial triangle, Preprint, 
               2008.
%D A008301 R. L. Graham and Nan Zang, Enumerating split-pair arrangements, J. Combin. 
               Theory, Ser. A, 115 (2008), pp. 293-303.
%F A008301 Recurrence relations are given on p. 370 of the Poupard paper; however, 
               in line -5 the summation index should be k and in line -4 the expression 
               2_h^{k-1} should be replaced by 2d_h^(k-1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               May 03 2004
%F A008301 If we write the triangle like this:
%F A008301 .............0, ...1, ..0
%F A008301 .........0, ..1, ...2, ..1, ..0
%F A008301 .....0, ..4, ..8, ..10, ..8, ..4, ..0
%F A008301 .0, .34, .68, .94, .104, .94, .68, .34, .0
%F A008301 then the first nonzero term is the sum of the previous row
%F A008301 and the remaining terms in each row are obtained by the rule illustrated 
               by 104 = 2*94 - 2*8 - 1*68. - N. J. A. Sloane (njas(AT)research.att.com), 
               Jun 10 2005
%e A008301 [1], [1, 2, 1], [4, 8, 10, 8, 4], [34, 68, 94, 104, 94, 68, 34], [496, 
               992, 1420, 1712, 1816, 1712, 1420, 992, 496], [11056, 22112, 32176, 
               40256, 45496, 47312, 45496, 40256, 32176, 22112, 11056], [349504, 
               699008, 1026400, 1309568, 1528384, 1666688, 1714000, 1666688, 1528384, 
               1309568, 1026400, 699008, 349504], ...
%Y A008301 Cf. A107652. Leading diagonal and row sums = A002105.
%Y A008301 Sequence in context: A112173 A058543 A156817 this_sequence A113820 A133267 
               A145864
%Y A008301 Adjacent sequences: A008298 A008299 A008300 this_sequence A008302 A008303 
               A008304
%K A008301 nonn,tabf,easy,nice
%O A008301 0,3
%A A008301 N. J. A. Sloane (njas(AT)research.att.com).
%E A008301 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2004