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%I #21 Sep 08 2022 08:44:33
%S 1,66,3366,154836,6735366,282885372,11598300252,467245810152,
%T 18573020953542,730538824172652,28491014142733428,1103379274982221848,
%U 42480102086815541148,1627314679941087653208,62070431363467200486648,2358676391811753618492624,89334868339870168300408134
%N a(n) = (6^n/n!) * Product_{k=0..n-1} ( 6*k + 11 ).
%H G. C. Greubel, <a href="/A004998/b004998.txt">Table of n, a(n) for n = 0..635</a>
%F G.f.: (1 - 36*x)^(-11/6).
%F a(n) ~ 6/5*Gamma(5/6)^-1*n^(5/6)*6^(2*n)*{1 + 55/72*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
%F D-finite with recurrence: n*a(n) +6*(-6*n-5)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020
%p a:= n-> (6^n/n!)*product(6*k+11, k=0..n-1); seq(a(n), n=0..20); # _G. C. Greubel_, Aug 22 2019
%t CoefficientList[Series[(1-36x)^(-11/6),{x,0,20}],x] (* or *) Table[(36^(n-1) Pochhammer[11/6,n-1])/Gamma[n],{n,20}] (* _Harvey P. Dale_, Jul 24 2011 *)
%o (PARI) a(n) = (6^n/n!)*prod(k=0, n-1, 6*k+11);
%o vector(20, n, n--; a(n)) \\ _G. C. Greubel_, Aug 22 2019
%o (Magma) [1] cat [6^n*(&*[6*k+11: k in [0..n-1]])/Factorial(n): n in [1..20]]; // _G. C. Greubel_, Aug 22 2019
%o (Sage) [6^(2*n)*rising_factorial(11/6, n)/factorial(n) for n in (0..20)] # _G. C. Greubel_, Aug 22 2019
%o (GAP) List([0..20], n-> 6^n*Product([0..n-1], k-> 6*k+11)/Factorial(n) ); # _G. C. Greubel_, Aug 22 2019
%K nonn,easy
%O 0,2
%A Joe Keane (jgk(AT)jgk.org)
%E Terms a(14) onward added by _G. C. Greubel_, Aug 22 2019
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