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A052795 a(n) = (6*n)!/(5*n+1)!. 3
1, 1, 12, 306, 12144, 657720, 45239040, 3776965920, 371090522880, 41951580652800, 5364506808460800, 765606216965990400, 120639963305775513600, 20803502274492921984000, 3896911902445736638464000, 787971434323820421362688000, 171063718698166603304067072000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Old name was: A simple grammar.
LINKS
FORMULA
E.g.f.: RootOf(-_Z+_Z^6*x+1).
D-finite Recurrence: {a(1)=1, a(2)=12, (-720-9864*n-48600*n^2-110160*n^3-116640*n^4-46656*n^5)*a(n)+(3125*n^4+9375*n^3+10000*n^2+4500*n+720)*a(n+1), a(6)=45239040, a(3)=306, a(4)=12144, a(5)=657720}.
1/25*3^(1/2)*(5+5^(1/2))^(1/2)*(5-5^(1/2))^(1/2)*Pi^(1/2) *GAMMA(2*n+37/3) *GAMMA(2*n+38/3)/GAMMA(n+34/5)/GAMMA(n+33/5)/GAMMA(n+32/5) /GAMMA(n+36/5) *GAMMA(n+13/2)*3125^(-6-n)*2916^(n+6).
a(n) = (6*n)!/(5*n+1)!. - Mark van Hoeij, May 29 2013
E.g.f.: exp( 1/6 * Sum_{k>=1} binomial(6*k,k) * x^k/k ). - Seiichi Manyama, Feb 08 2024
a(n) = A000142(n)*A002295(n). - Alois P. Heinz, Feb 08 2024
MAPLE
spec := [S, {B=Prod(Z, S, S, S, S, S), S=Sequence(B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
seq((6*n)!/(5*n+1)!, n=0..20); # Mark van Hoeij, May 29 2013
PROG
(PARI) a(n) = (6*n)!/(5*n+1)!; \\ Joerg Arndt, May 29 2013
(Python)
from sympy import ff
def A052795(n): return ff(6*n, n-1) # Chai Wah Wu, Sep 01 2023
CROSSREFS
Sequence in context: A309319 A358327 A054942 * A304126 A263668 A053064
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using Mark van Hoeij's formula from Joerg Arndt, Feb 18 2019
Accidentally removed a(0) reinserted by Georg Fischer, May 09 2021
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)