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

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

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: A174986 A327671 A036563 * A321716 A245567 A337419

Adjacent sequences: A025261 A025262 A025263 * A025265 A025266 A025267

Keyword

nonn

Author

Clark Kimberling

Status

approved