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%I #10 Oct 25 2023 23:59:43
%S 1,1,1,2,6,18,72,360,1800,10800,75600,529200,4233600,38102400,
%T 342921600,3429216000,37721376000,414935136000,4979221632000,
%U 64729881216000,841488455808000,11780838381312000,176712575719680000
%N Ratios of successive terms are 1,1,2,3,3,4,5,5,6,7,7,...
%H Robert Israel, <a href="/A004395/b004395.txt">Table of n, a(n) for n = 0..431</a>
%F G.f.: hypergeom([1/2, 1/2, 1, 1], [], 8*x^3) + x*hypergeom([1/2, 1, 1, 3/2], [], 8*x^3) + x^2*hypergeom([1, 1, 3/2, 3/2], [], 8*x^3). - _Robert Israel_, Aug 05 2020
%p G:=hypergeom([1/2, 1/2, 1, 1], [], 8*x^3) + x*hypergeom([1/2, 1, 1, 3/2], [], 8*x^3) + x^2*hypergeom([1, 1, 3/2, 3/2], [], 8*x^3):
%p S:= series(G,x,41):
%p seq(coeff(S,x,n),n=0..40); # _Robert Israel_, Aug 05 2020
%Y a(n+1) = a(n) * A004396(n).
%K nonn
%O 0,4
%A _N. J. A. Sloane_
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