A247169 G.f. (4*x+3)/(2*(x+1))*(1+1/sqrt(-4*x^4-4*x^3+1)).

3, 1, -1, 4, 3, 1, 8, 22, 11, 31, 99, 111, 144, 456, 734, 904, 2155, 4285, 5921, 11173, 23603, 37489, 63161, 129031, 227072, 375376, 719432, 1335478, 2264118, 4126266, 7759608, 13613744, 24219051, 45127317, 81256395, 144053547, 264457881

Offset: 0

Author

Vladimir Kruchinin, Nov 21 2014

Keywords

• sign

Crossrefs

Cf. A025277

Programs

Maple

A247169 := proc(n)
    if n = 0 then
        3;
    else
        add( binomial(n-2*m,m)*binomial(2*m-1,n-2*m-1)/(n-2*m),m=0..floor((n-1)/2)) ;
        n*% ;
    end if;
end proc:
seq(A247169(n),n=0..50) ;

Maxima

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));

Formula

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.

G.f.: A(x)=x*B'(x)/B(x), where B(x) is g.f. of A025277.

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