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 A213406 G.f.: exp( Sum_{n>=1} binomial(12*n-1, 6*n) * x^n/n ). 4
 1, 462, 782761, 1841287756, 5032296741620, 14989560797138774, 47213445715209298574, 154652100584276167220568, 521484200609508028036469644, 1798155951370712836530932544856, 6311247529513572335576033066558569, 22473253520120296968203645006140445948 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..275 Feihu Liu and Guoce Xin, Simple Generating Functions for Certain Young Tableaux with Periodic Walls, arXiv:2401.14627 [math.CO], 2024. FORMULA G.f. A(x) satisfies: A(x^6) = C(x)*C(u*x)*C(u^2*x)*C(u^3*x)*C(u^4*x)*C(u^5*x) where u = exp(2*Pi*I/6) and C(x) = (1-sqrt(1-4*x))/(2*x) is the Catalan function (A000108). a(n) ~ (2-sqrt(2)) * (2-sqrt(2)*3^(1/4)) * (sqrt(3)-1) * 8^(4*n+1) / (n^(3/2)*sqrt(3*Pi)). - Vaclav Kotesovec, Jul 05 2014 EXAMPLE G.f.: A(x) = 1 + 462*x + 782761*x^2 + 1841287756*x^3 + 5032296741620*x^4 +... such that A(x^6) = C(x)*C(u*x)*C(u^2*x)*C(-x)*C(-u*x)*C(-u^2*x) where u = exp(2*Pi*I/6) and C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 + 429*x^7 +... Also, A(x^6) = G(x^3)*G(-x^3) where G(x) is the g.f. of A213403: G(x) = 1 + 10*x + 281*x^2 + 10580*x^3 + 457700*x^4 + 21475122*x^5 +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, binomial(12*m-1, 6*m)*x^m/m)+x*O(x^n)), n)} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A000108, A079489, A213403, A213404, A213405. Sequence in context: A208619 A318266 A295432 * A294853 A025038 A028684 Adjacent sequences: A213403 A213404 A213405 * A213407 A213408 A213409 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 10 2012 STATUS approved

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Last modified April 22 22:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)