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

1,1

Links

Table of n, a(n) for n=1..25.

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

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 *)

Prog

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

Crossrefs

Cf. A025266.

Sequence in context: A327671 A036563 A380610 * A321716 A375527 A245567

Adjacent sequences: A025261 A025262 A025263 * A025265 A025266 A025267

Keyword

nonn

Author

Clark Kimberling

Status

approved