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%I #21 Jan 27 2024 07:52:56
%S 0,1,0,1,4,19,96,511,2832,16215,95374,573837,3520228,21961119,
%T 139038824,891817687,5787091552,37946582995,251173847170,
%U 1676831257693,11282156358500,76453813499219,521508969157826,3578990500062417,24700214881378152,171359711873508367
%N Dimension of totally primitive elements of the algebra "Baxter" of order n.
%D S. Giraudo, Algebraic and combinatorial structures on pairs of twin binary trees, Journal of Algebra, Volume 360, 15 June 2012, Pages 115-157.
%H S. Giraudo, <a href="https://doi.org/10.46298/dmtcs.2919">Algebraic and combinatorial structures on Baxter permutations</a>, DMTCS proc. AO, FPSAC 2011 Rykjavik, (2011) 387-398.
%F Giraudo gives a generating function.
%o (PARI)
%o baxter(n) = sum(k=1, n, binomial(n+1, k-1) * binomial(n+1, k) * binomial(n+1, k+1) / (binomial(n+1, 1) * binomial(n+1, 2)));
%o lista(m) = {u = t + t*O(t^m); b = 1 + sum(n=1, m, baxter(n)*u^n); gfbt = (b-1)/b^2; for (n=0, m, print1(polcoeff(gfbt, n, t), ", "));}
%o \\ _Michel Marcus_, Feb 16 2013
%Y Cf. A001181.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Oct 03 2012
%E More terms from _Michel Marcus_, Feb 16 2013