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 A217216 Dimension of algebraic generators of the algebra "Baxter" of order n. 0
 0, 1, 1, 3, 11, 47, 221, 1113, 5903, 32607, 186143, 1092015, 6555515, 40137219, 249984481, 1580468321, 10125395007, 65639436955, 430048061915, 2844592155631, 18979693010495, 127641472658231, 864645413540671, 5896221199266519, 40455246946190079 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..24. G. Chatel and V. Pilaud, Cambrian Hopf Algebras, arXiv:1411.3704 [math.CO], 2014-2015. S. Giraudo, Algebraic and combinatorial structures on Baxter permutations, DMTCS proc. AO, FPSAC 2011 Rykjavik, (2011) 387-398 S. Giraudo, Algebraic and combinatorial structures on pairs of twin binary trees, arXiv:1204.4776 [math.CO], 2012. S. Giraudo, Algebraic and combinatorial structures on pairs of twin binary trees, Journal of Algebra, Volume 360, 15 June 2012, Pages 115-157. FORMULA Giraudo gives a generating function. a(n) ~ c * 8^n / n^4, where c = 4.21514033443045415032... - Vaclav Kotesovec, Apr 27 2024 MATHEMATICA nmax = 25; 1-1/(1+Sum[HypergeometricPFQ[{-1-n, 1-n, -n}, {2, 3}, -1] x^n, {n, nmax}]) + O[x]^nmax // CoefficientList[#, x]& (* Jean-François Alcover, Sep 26 2018 *) PROG (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); gfbc = 1 - 1/b; for (n=0, m, print1(polcoeff(gfbc, n, t), ", ")); } \\ Michel Marcus, Feb 16 2013 CROSSREFS Cf. A001181. Sequence in context: A262607 A059284 A118927 * A301409 A295539 A359120 Adjacent sequences: A217213 A217214 A217215 * A217217 A217218 A217219 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 03 2012 EXTENSIONS More terms from Michel Marcus, Feb 16 2013 STATUS approved

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Last modified August 8 06:39 EDT 2024. Contains 375020 sequences. (Running on oeis4.)