A045740 Number of components in all forests on nodes on a circle.

1, 3, 12, 62, 370, 2397, 16345, 115376, 834786, 6152285, 45990120, 347673108, 2652283517, 20385035972, 157656007680, 1225743120520, 9572972899946, 75056029550721, 590469939950716, 4659115833115680, 36859770507695688

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

Sum(k*binomial(n, k-1)*binomial(3*n-2*k-1, n-k)/(2*n-k), k=1..n)

Conjecture D-finite with recurrence -2*(n-1)*(2*n-1) *(7912210314*n^2 +24034951267*n -109031255382)*a(n) +2*(-15824420628*n^4 +759853283620*n^3 -1653756416501*n^2 -3170366114943*n +6074871939666) *a(n-1) +2*(1171007126472*n^4 -5580539787848*n^3 -21281457754861*n^2 +151349953543323*n -205322404158756) *a(n-2) +(530118091038*n^4 -3085109917817*n^3 -8408054715093*n^2 +76142928591932*n -101713943817720) *a(n-3)

-15*(n-3)*(n-6) *(23736630942*n^2 +73277266499*n-235582184233)*a(n-4)=0. - R. J. Mathar, Jul 22 2022

Maple

A045740 := proc(n)
    local k ;
    add(k*binomial(n, k-1)*binomial(3*n-2*k-1, n-k)/(2*n-k) , k=1..n) ;
end proc:
seq(A045740(n), n=1..30) ; # R. J. Mathar, Jul 22 2022

Crossrefs

Sequence in context: A258798 A369709 A074516 * A187820 A074529 A143916

Adjacent sequences: A045737 A045738 A045739 * A045741 A045742 A045743

Keyword

nonn

Author

Emeric Deutsch

Status

approved