The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A213404 G.f.: exp( Sum_{n>=1} binomial(8*n-1, 4*n) * x^n/n ). 4
1, 35, 3830, 570451, 98118690, 18345127262, 3621992085708, 743083237338755, 156855468465746346, 33846364485841559594, 7432235142547456907188, 1655432795976620159935790, 373110570133205997324473492, 84936332285861009708851200092, 19500719075082334054293510927128 (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^4) = C(x)*C(-x)*C(I*x)*C(-I*x) where C(x) = (1-sqrt(1-4*x))/(2*x) is the Catalan function (A000108).
a(n) ~ (1-sqrt(2*(sqrt(2)-1))) * 4^(4*n+1) / (n^(3/2)*sqrt(Pi)). - Vaclav Kotesovec, Jul 05 2014
EXAMPLE
G.f.: A(x) = 1 + 35*x + 3830*x^2 + 570451*x^3 + 98118690*x^4 +...
such that A(x^4) = C(x)*C(-x)*C(I*x)*C(-I*x) where I^2 = -1 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^2) = G(x)*G(-x) where G(x) is the g.f. of A079489:
G(x) = 1 + 3*x + 22*x^2 + 211*x^3 + 2306*x^4 + 27230*x^5 + 338444*x^6 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, binomial(8*m-1, 4*m)*x^m/m)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A343586 A201725 A202578 * A249887 A210314 A294851
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 May 26 01:03 EDT 2024. Contains 372806 sequences. (Running on oeis4.)