0,3

a(n) = K(2,2; n)/2 with K(a,b; n) defined in a comment to A068763.

a(n) = (2^n)*p(n, -1/2) with the row polynomials p(n, x) defined from array A068763.

a(n+1) = 2*sum(a(k)*a(n-k), k=0..n), n>=1, a(0) = 1 = a(1).

G.f.: (1-sqrt(1-8*x*(1-x)))/(4*x).

E.g.f. (offset -1) is exp(4*x)*BesselI(1, 2*sqrt(2)*x)/(sqrt(2)*x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 31 2004

The o.g.f. satisfies A(x)= 1 + x*(2*A(x)^2 -1), A(0)=1. W. Lang, Nov 13 2007.

a(n)= subs(t=1,diff((-1+2*t^2)^n,t$(n-1)))/n!, n>=2, due to the Lagrange series for the given implicit o.g.f. equation. This formula holds also for n=1 if no differentiation is used. W. Lang, Nov 13 2007, Feb 22 2008

(PARI) {a(n)= local(A); if(n<1, n==0, n--; A= x*O(x^n); n!*simplify(polcoeff( exp(4*x +A)* besseli(1, 2*x* quadgen(8) +A), n)))} /* Michael Somos Mar 31 2007 */

Cf. A025227-A025230.

Cf. A071356, A001003, A025235.

Sequence in context: A083879 A081671 A006629 this_sequence A127394 A046984 A129323

Adjacent sequences: A068761 A068762 A068763 this_sequence A068765 A068766 A068767

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 04, 2002