A247169 - OEIS

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..36.

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

MAPLE

A247169 := proc(n)

if n = 0 then

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) ;

PROG

(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));