A025264 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4, starting 2,1,1.

2, 1, 1, 5, 22, 99, 450, 2067, 9586, 44852, 211570, 1005427, 4810460, 23157904, 112110906, 545524287, 2666864340, 13092764136, 64527778938, 319157531592, 1583724160896, 7882364163954, 39339994155288, 196843821874407, 987272738842392

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A025266.

Programs

Maple

A025264 := proc(n)
    option remember ;
    if n < 4 then
        op(n,[2,1,1]) ;
    else
        add( procname(i)*procname(n-i),i=1..n-1) ;
    end if;
end proc:
seq(A025264(n),n=1..20) ; # R. J. Mathar, Jan 13 2025

Mathematica

nmax = 30; aa = ConstantArray[0,nmax]; aa[[1]] = 2; aa[[2]] = 1; aa[[3]] = 1; Do[aa[[n]] = Sum[aa[[k]] * aa[[n-k]],{k,1,n-1}],{n,4,nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)

PARI

a(n)=polcoeff((1-sqrt(1-8*x+12*x^2+12*x^3+x*O(x^n)))/2,n)

Formula

G.f.: (1-sqrt(1-8*x+12*x^2+12*x^3))/2. - Michael Somos, Jun 08 2000

Recurrence: n*a(n) = 4*(2*n-3)*a(n-1) - 12*(n-3)*a(n-2) - 6*(2*n-9)*a(n-3). - Vaclav Kotesovec, Jan 25 2015