A217217 Dimension of totally primitive elements of the algebra "Baxter" of order n.

0, 1, 0, 1, 4, 19, 96, 511, 2832, 16215, 95374, 573837, 3520228, 21961119, 139038824, 891817687, 5787091552, 37946582995, 251173847170, 1676831257693, 11282156358500, 76453813499219, 521508969157826, 3578990500062417, 24700214881378152, 171359711873508367

Offset: 0

Author

N. J. A. Sloane, Oct 03 2012

Keywords

• nonn

References

• S. Giraudo, Algebraic and combinatorial structures on pairs of twin binary trees, Journal of Algebra, Volume 360, 15 June 2012, Pages 115-157.

Links

• S. Giraudo, Algebraic and combinatorial structures on Baxter permutations, DMTCS proc. AO, FPSAC 2011 Rykjavik, (2011) 387-398.

Crossrefs

Cf. A001181.

Programs

PARI

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)));
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), ", "));}
\\ Michel Marcus, Feb 16 2013

Formula

Giraudo gives a generating function.

Extensions

More terms from Michel Marcus, Feb 16 2013