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A259974 Irregular triangle read by rows: T(n,k) = number of meanders with n bridges in which the first bridge is bridge k.

%I A259974 #19 Jun 28 2017 15:19:06
%S A259974 1,1,1,1,2,1,3,2,3,8,3,3,14,7,7,14,42,14,11,14,81,36,28,36,81,262,81,
%T A259974 57,57,81,538,221,155,155,221,538,1828,538,353,316,353,538,3926,1530,
%U A259974 1003,902,1003,1530,3926,13820,3926,2458,2053,2053,2458,3926,30694,11510,7214,6059,6059,7214,11510,30694,110954,30694,18575,14810,13827,14810,18575,30694
%N A259974 Irregular triangle read by rows: T(n,k) = number of meanders with n bridges in which the first bridge is bridge k.
%D A259974 Lando, S. K. and Zvonkin, A. K. Plane and projective meanders. Conference on Formal Power Series and Algebraic Combinatorics (Bordeaux, 1991).
%D A259974 Lando, S. K. and Zvonkin, A. K. Meanders. In Selected translations. Selecta Math. Soviet. 11 (1992), no. 2, 117-144.
%H A259974 Andrew Howroyd, <a href="/A259974/b259974.txt">Table of n, a(n) for n = 1..420</a>
%H A259974 S. K. Lando and A. K. Zvonkin , <a href="/A005316/a005316_1.pdf">Plane and projective meanders</a>, Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303. (Annotated scanned copy)
%H A259974 S. K. Lando and A. K. Zvonkin, <a href="http://dx.doi.org/10.1016/0304-3975(93)90316-L">Plane and projective meanders</a>, Theoretical Computer Science Vol. 117 (1993), no. 1-2, 227-241.
%e A259974 Triangle begins:
%e A259974 1,
%e A259974 1,
%e A259974 1,1,
%e A259974 2,1,
%e A259974 3,2,3,
%e A259974 8,3,3,
%e A259974 14,7,7,14,
%e A259974 42,14,11,14,
%e A259974 81,36,28,36,81,
%e A259974 262,81,57,57,81,
%e A259974 538,221,155,155,221,538,
%e A259974 ...
%Y A259974 Diagonals are A005316, A006660, A006661, A006662. Cf. A008828.
%K A259974 nonn,tabf
%O A259974 1,5
%A A259974 _N. J. A. Sloane_, Jul 12 2015
%E A259974 T(12,k)-T(40,k) from _Andrew Howroyd_, Dec 15 2015