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A052795
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a(n) = (6*n)!/(5*n+1)!.
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3
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1, 1, 12, 306, 12144, 657720, 45239040, 3776965920, 371090522880, 41951580652800, 5364506808460800, 765606216965990400, 120639963305775513600, 20803502274492921984000, 3896911902445736638464000, 787971434323820421362688000, 171063718698166603304067072000
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listen;
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OFFSET
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0,3
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COMMENTS
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Old name was: A simple grammar.
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LINKS
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FORMULA
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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).
E.g.f.: exp( 1/6 * Sum_{k>=1} binomial(6*k,k) * x^k/k ). - Seiichi Manyama, Feb 08 2024
E.g.f. satisfies A(x) = 1/(1 - x*A(x)^5).
a(n) = Sum_{k=0..n} (5*n+1)^(k-1) * |Stirling1(n,k)|. (End)
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MAPLE
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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
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PROG
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(PARI) a(n) = (6*n)!/(5*n+1)!; \\ Joerg Arndt, May 29 2013
(Python)
from sympy import ff
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CROSSREFS
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KEYWORD
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easy,nonn,changed
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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Accidentally removed a(0) reinserted by Georg Fischer, May 09 2021
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STATUS
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approved
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