0,3

C. Poupard, Deux proprietes des arbres binaires ordonnes stricts, European J. Combin., 10 (1989), 369-374.

Dominique Foata and Guo-Niu Han, Dimers and new q-tangent numbers, Preprint, 2008.

Dominique Foata and Guo-Niu Han, The dimer polynomial triangle, Preprint, 2008.

R. L. Graham and Nan Zang, Enumerating split-pair arrangements, J. Combin. Theory, Ser. A, 115 (2008), pp. 293-303.

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

If we write the triangle like this:

.............0, ...1, ..0

.........0, ..1, ...2, ..1, ..0

.....0, ..4, ..8, ..10, ..8, ..4, ..0

.0, .34, .68, .94, .104, .94, .68, .34, .0

then the first nonzero term is the sum of the previous row

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

[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], ...

Cf. A107652. Leading diagonal and row sums = A002105.

Sequence in context: A112173 A058543 A156817 this_sequence A113820 A133267 A145864

Adjacent sequences: A008298 A008299 A008300 this_sequence A008302 A008303 A008304

nonn,tabf,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 03 2004