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a(n) = round(3F2([1, 3/2, 1 - n], [2, 2], -4)).
1

%I #7 Jul 27 2022 06:52:38

%S 0,1,3,7,24,87,332,1320,5407,22672,96844,419910,1843386,8176962,

%T 36594388,165026353,749170529,3420949803,15702232962,72407225094,

%U 335276107549,1558289108596,7267201176311,33996105203757,159484982985619,750134031377432

%N a(n) = round(3F2([1, 3/2, 1 - n], [2, 2], -4)).

%C Without rounding, the sequence were 1, 5/2, 22/3, 97/4, 436/5, 997/3, 9241/7, 43257/8,... for n>=1. - _R. J. Mathar_, Jul 27 2022

%F a(n) = A129164(n)/n for n>=1.

%o (Sage)

%o A246657 = lambda n: hypergeometric([1, 3/2, 1-n], [2, 2], -4)

%o [round(A246657(n).n(100)) for n in (0..25)]

%Y Cf. A129164.

%K nonn

%O 0,3

%A _Peter Luschny_, Sep 16 2014