login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A208619 A318266 A295432 * A294853 A025038 A028684
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 10 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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