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%I #18 Feb 16 2020 04:59:54
%S 3,1,-1,4,3,1,8,22,11,31,99,111,144,456,734,904,2155,4285,5921,11173,
%T 23603,37489,63161,129031,227072,375376,719432,1335478,2264118,
%U 4126266,7759608,13613744,24219051,45127317,81256395,144053547,264457881
%N G.f. (4*x+3)/(2*(x+1))*(1+1/sqrt(-4*x^4-4*x^3+1)).
%F a(n) = n*sum_{m=0..(n-1)/2} binomial(n-2*m,m)*binomial(2*m-1,n-2*m-1)/(n-2*m), n>0, a(0)=3.
%F G.f.: A(x)=x*B'(x)/B(x), where B(x) is g.f. of A025277.
%F D-finite with recurrence: 3*n*a(n) +(7*n-8)*a(n-1) +4*(n-2)*a(n-2) +6*(-2*n+3)*a(n-3) +2*(-20*n+49)*a(n-4) +4*(-11*n+36)*a(n-5) +16*(-n+4)*a(n-6)=0. - _R. J. Mathar_, Nov 25 2014, corrected Feb 16 2020
%p A247169 := proc(n)
%p if n = 0 then
%p 3;
%p else
%p add( binomial(n-2*m,m)*binomial(2*m-1,n-2*m-1)/(n-2*m),m=0..floor((n-1)/2)) ;
%p n*% ;
%p end if;
%p end proc:
%p seq(A247169(n),n=0..50) ;
%o (Maxima)
%o a(n):=if n=0 then 3 else (n*sum((binomial(n-2*m,m)*binomial(2*m-1,n-2*m-1))/(n-2*m),m,0,(n-1)/2));
%Y Cf. A025277
%K sign
%O 0,1
%A _Vladimir Kruchinin_, Nov 21 2014