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%I #12 Apr 26 2023 18:31:45
%S 1,1,6,57,622,7338,91144,1174281,15548694,210295326,2892818244,
%T 40347919626,569274150156,8110508473252,116518215264492,
%U 1686062250699433,24552388991392230,359526085719652662,5290709340633314596,78201907647506243758,1160507655117628665252,17283862221822154612428,258257655550682547281952
%N A bisection of A000957.
%F a(n) = A000957(2*n+1).
%p b:= proc(n) option remember; `if`(n<3, n*(2-n),
%p ((7*n-12)*b(n-1)+(4*n-6)*b(n-2))/(2*n))
%p end:
%p a:= n-> b(2*n+1):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Apr 26 2023
%o (PARI)
%o x='x+O('x^100); v=Vec((1-sqrt(1-4*x))/(3-sqrt(1-4*x)));
%o vector(#v\2,n,v[2*n-1]) /* show terms */
%o (Python)
%o from itertools import count, islice
%o def A138414_gen(): # generator of terms
%o yield 1
%o a, c = 0, 1
%o for n in count(1,2):
%o yield (a:=(c:=c*((n<<2)+2)//(n+2))-a>>1)
%o a=(c:=c*((n+1<<2)+2)//(n+3))-a>>1
%o A138414_list = list(islice(A138414_gen(),20)) # _Chai Wah Wu_, Apr 26 2023
%Y Cf. A000957, A138413.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 08 2008
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